Chapter 4: MeanVariance Analysis


 Kerry Blake
 2 years ago
 Views:
Transcription
1 Chapter 4: MeanVariance Analyi Modern portfolio theory identifie two apect of the invetment problem. Firt, an invetor will want to maximize the expected rate of return on the portfolio. Second, an invetor will want to minimize the rik of the portfolio. The two apect amount to the objective of maximizing the expected rate of return for any given, acceptable, level of rik. Alternatively the objective can be tated a: minimize the rik for any given, acceptable, level of expected return. For the purpoe here, rik i aociated with the variance  or more commonly, the tandard deviation  of the portfolio. The goal of ection 4.1 i to contruct the efficient frontier. Every point on the frontier will contitute a poible portfolio which meet the objective of maximum return for a given rik (or, minimum rik for a given return). Once the frontier i identified, then ection 4. addree the quetion of how an individual invetor will chooe among the variou efficient portfolio. The invetor preference decribe how they are willing to tradeoff higher return for lower rik, while the efficient frontier decribe how they are able to make the tradeoff. Hence, without knowing the invetor preference, we cannot determine which efficient portfolio will be choen. Our job i only to contruct the efficient frontier, then let the invetor decide where they would like to be on it. 1 Section 4.3 introduce a rikfree aet, which turn out to have important implication. The introduction of a rikfree aet allow the invetor to eparate the quetion of identifying the optimum riky portfolio from hi/her own preference a reult known a the Separation Theorem. Section 4.4 recount the context and original development of the eparation theorem. A word of caution i in order before beginning. In order to keep the calculation in the example down to a manageable number, we will be contructing a portfolio from only two riky aet (and adding one rikfree aet in ection 4.3). The reult obtained will generalize to any number of aet. The reult and their interpretation will be tated in the generalized form. In doing o, the explanation may appear to train the actual numerical reult. 4.1 Contruction of the Efficient Frontier reviouly, we had been concerned with variou way in which to think about the determination of aet price (e.g., treat aet a tock or flow). Since aet price are forward looking, the quetion of how expectation are formed kept ariing. A high aet price implied holding other thing uch a rik of default and liquidity contant a high expected payoff. The focu wa on buying an aet with a high expected payoff and a other did thi, then the price would be driven upward. Harry Markowtiz wa the firt to ytematically elevate the iue of rik to a poition on par with expected return. The efficient frontier illutrate the tradeoff that exit between expected return and rik. In the contruction of the frontier, we will dicover the 1 The connection to conumer theory of tandard microeconomic hould become abundantly clear. The conumer attempt to maximize utility a decribed by hi/her indifference curve. The indifference curve illutrate how the conumer i willing to trade one good for another. The budget contraint decribe how the conumer i able to trade one good for another given relative price of the good. Aet price are forward looking in the ene that they depend upon what the future i expected to be i.e., what tate of the world actually come to pa. 1
2 benefit of diverification. A imple example will be ued to demontrate the procedure of contructing the efficient frontier. The efficient frontier hould be contructed from a large number of poible aet. However, in order to illutrate the baic procedure, it will be ueful to limit the cope of the aet to two. Suppoe an invetor ha a total of $100,000 to invet in a tock and/or bond it might be preferable to think of thee a index fund. The invetor mut decide how much of the $100,000 to invet in the tock and how much to invet in the bond. Thi deciion will determine the invetor portfolio (i.e., collection of aet). The characteritic of each aet are given in table 5.1. Table 5.1 Stock ond E(r) 7.50% 5.00% σ 1.50% 5.00% ρ 1 Suppoe the invetor held only the bond. The expected return would be 5% with a tandard deviation of 5%. Diatified with thi return and willing to take on more rik if neceary, the invetor ell ome bond and invet in the tock. Suppoe the invetor new portfolio contained 30% tock and 70% bond. What i the expected rate of return on the invetor portfolio? Recall that the expected rate of return on a portfolio i merely the weighted average of the individual rate of return where the weight are the percentage of the aet in the portfolio. (4.1) E r ) = W E( r ) + W E( r ) ( p The W repreent the weight (or, percentage of the aet in the portfolio) and ubcript S and refer to tock and bond repectively. In our example, the expected rate of return on the portfolio i calculated a follow. (4.) E ( r ) W E( r ) + W E( r ) = (.3)(7.5) + (.7)(5) = 5.75% p = Hence, the invetor ha been able to increae the expected rate of return on the portfolio by holding ome tock. What wa the cot of obtaining the higher expected rate of return? The invetor may have believed that he would have to take on more rik (i.e., higher tandard deviation) to obtain a higher expected return. However, did rik increae? In order to calculate the tandard deviation of the portfolio we begin by calculating the variance of a portfolio. 3 (4.3) σ = ( W σ ) + ( W σ ) + W W σ σ ρ 3 The derivation of thi equation i given in the mathematical and tatitical appendix.
3 Recall, the Greek letter rho (ρ) i the correlation coefficient which when multiplied by the two tandard deviation equal the covariance between the two aet. The important point to notice about the above equation for the variance i that unlike the expected rate of return it i not at leat not alway the imple weighted average of the individual variance. 4 In our example, the variance of the portfolio compoed of 30% tock and 70% bond i the following. (4.4) σ = ( W σ ) + ( W σ ) + W W σ σ ρ = [(.3)(1.5)] + [(.7)(5)] + (.3)(.7)(1.5)(5)( 1) =.065 The tandard deviation of the portfolio (i.e., our meaure of rik) i the quare root of the variance. (4.5) σ σ =.065 =.5% = y adding an aet (i.e., the tock) with a higher rate of return and rik to hi bondonly portfolio our invetor ha been able to increae the expected rate of return not very urpriing and reduce the overall rik of the portfolio thi i very urpriing. Here we ee our firt indication of the power of diverification. In addition, we ee that the bondonly portfolio wa not a very efficient portfolio. That i, there i at leat one portfolio available the one we ued with higher expected return and lower rik. ractice 1. Suppoe the invetor liked what he aw happened o much that he decided to place $70,000 (or, 70%) in the tock and $30,000 (or, 30%) in the bond. What i the expected rate of return and tandard deviation (rik) of thi portfolio? {{{Anwer 1. E ( r ) W E( r ) + W E( r ) = (.7)(7.5) + (.3)(5) = 6.75% p = σ = ( W σ ) + ( W σ ) + W W σ σ ρ = [(.7)(1.5)] + [(.3)(5)] σ σ = 5.56 = 7.5% }}} = + (.7)(.3)(1.5)(5)( 1) = 5.56 Suppoe our invetor having tried three different portfolio (bondonly, 30% tock and 70% bond, 70% tock and 30% bond) realized that the reult were changing in uncertain way. Moving from the bondonly to 30%70% tockbond portfolio the rate of return increaed and the rik decreaed. Moving more into tock, the rate of return continued to increae, but o did the rik. Table 5. might help the invetor begin to ee ome pattern in the variou portfolio. 4 The appendix contain further commentary on thi point. 3
4 TALE 5. Stock ond Return (%) Rik (%) 100% 0% % 5% % 10% % 15% % 0% % 5% % 30% % 35% % 40% % 45% % 50% % 55% % 60% 6 35% 65% % 70% % 75% % 80% % 85% % 90% % 95% % 100% 5 5 What are the implication of thi analyi? Firt, think of beginning with the bondonly portfolio. The expected rate of return i 5% with a tandard deviation of 5%. Now, uppoe the invetor decide to allocate 95% of the total invetment in the bond and 5% in the tock. The expected return will increae to 5.13% and the tandard deviation (rik) will actually decreae to 4.13%! Surely, the bondonly portfolio i not efficient. In other word, if we can find another portfolio with a higher expected return and the ame  or, maller  tandard deviation, then the original portfolio hould not be choen regardle of the invetor preference. Second, notice that a we move up the table from the bottom row (where only the bond i held) the rik initially decline, then reache a minimum, then begin to increae. All along thi upward movement in the table, the expected rate of return i increaing. The implication can be clearly een in Figure 5.1. The efficient frontier conit of only the upper portion of the line. Thi upper portion conit of portfolio in which the expected rate of return can be increaed only at the cot of an increae in the tandard deviation (rik). We can graphically pick the efficient portfolio, chooe a given level of rik (i.e., pick a point on the horizontal axi), then move upward until the portfolio with the highet expected rate of return (i.e., move up from the horizontal axi to the highet point on the curved line) i reached. Alternatively, for a given expected rate of return (i.e., pick a point above the minimum rik, on 4
5 the vertical axi), chooe the portfolio which minimize rik (i.e., move to the right until you hit the curved line). Figure 5.1 The Efficient Frontier Return Rik Doing thi for all poibilitie, we would find that the efficient portfolio lie on the upper part of the chedule. 5 Though omewhat mileading, the efficient frontier may refer to the entire chedule. Undertood to mean thi, we find that in a two aet cae, each aet will lie on the frontier. In general, when the number of poible aet exceed two, no individual aet will be on the frontier again, the power of diverification. ractice. Suppoe an invetor contruct a portfolio with 0% in tock and 80% in bond. The invetor ha calculated the expected return on the tock to be 10% with a tandard deviation of 5%. The expected return on the bond i 6% with a tandard deviation of 1%. In addition, the correlation between tock and bond return i zero. Calculate the expected return and tandard deviation (rik) of thi portfolio. {{{Anwer. The expected rate of return on the portfolio will be: E(r ) = (.)(10) + (.8)(6) = 6.8% 5 The appendix provide the formula for the minimum tandard deviation. Given a correlation of 1, the minimum i quite traightforward to calculate it i zero. In addition, the appendix provide the equation for the weight to chooe in order to minimize the tandard deviation. For example, in the cae of a correlation of 1, the minimum tandard deviation (zero) will occur when the portfolio contain a percentage of bond equal to σ σ + σ. In our example, thi would be approximately 1.5/(1.5+5) =.71. Thu, in order to reduce the tandard deviation to zero, the invetor hould hold a portfolio coniting of 9% tock and 71% bond. 5
6 The variance of the portfolio i: σ = ( W σ ) + ( W σ ) + W W σ σ ρ = [(.)(5)] + [(.8)(1)] + (.)(.8)(5)(1)(0) = note, ince the correlation i zero, the lat term become zero a well. The tandard deviation (rik) of the portfolio i the quare root of the variance: σ = 10.8% In thi example, we have been able to reduce the rik below the rik of holding only the bond while increaing the rate of return on the portfolio above the bond rate of return.}}} What i the impact of the correlation coefficient? We will ue the example in ractice in order to tudy the role of the correlation coefficient. 6 However, we change the value of the correlation coefficient from 1 to +1. Notice that a long a the correlation coefficient i le than +1, diverification can lead to more efficient portfolio. In the unlikely event of the correlation coefficient being exactly +1, then the variance of the portfolio i equal to the weighted average of the individual variance jut like the expected rate of return of the portfolio. Thi implie that there will alway be a tradeoff between rik and return. The important point, however, i that the benefit of diverification do not hinge on a negative correlation between aet in a portfolio. However, clearly, there are greater benefit to be had with a negative correlation. The only condition for the benefit of diverification i that the aet do not move perfectly together (or, the cae of the correlation coefficient being exactly +1). The table indicate that the cloer the correlation coefficient come to 1, the greater will be the benefit of diverification. Thi can be een by chooing any portfolio containing both tock and bond (i.e., chooe a row in the table). Now, move acro the row from a correlation of +1 to 1. The expected rate of return of each portfolio in the row remain the ame (thi hould be clear from the calculation for expected rate of return of a portfolio). However, the tandard deviation (rik) continue to decreae! The far right hand ide of the table aume that tock and bond have a perfect negative correlation. In the cae of perfect negative correlation (i.e., 1) between two riky aet, it i alway poible to contruct a portfolio with zero tandard deviation (rik). In thi particular cae, if the portfolio contained approximately 3.4% tock and 67.6% bond, then the tandard deviation (rik) would be zero. The figure preent a graphical repreentation of thee idea. Moving from the figure with a correlation coefficient of +1 6 Recall that the correlation coefficient meaure the relationhip between two variable in our cae, the variable are the expected rate of return of the two aet. The correlation coefficient i cloely related to the covariance between two variable. However, the correlation coefficient i eaier to interpret. The cloer a correlation coefficient i to 1, the tronger the invere relationhip between the two variable. In the cae of exactly 1, we ay that the two variable are perfectly inverely related meaning that they alway move in oppoite direction. The cloer the correlation coefficient i to +1, the tronger i the poitive relationhip (i.e., they tend to move in the ame direction). A correlation coefficient cloe to zero implie a lack of relationhip between the two variable. 6
7 where the efficient frontier i a traight line indicating that the portfolio rate of return and tandard deviation are imply weighted average to the figure baed on a 1, the efficient frontier get pulled toward the vertical axi illutrating that rik i falling. 7
8 Table 5.3 Correlation = +1 Correlation = +0.5 Correlation = 0 Correlation = 0.5 Correlation = 1 Allocation ortfolio ortfolio ortfolio ortfolio ortfolio ortfolio ortfolio ortfolio ortfolio ortfolio Stock ond Return Rik Return Rik Return Rik Return Rik Return Rik
9 Efficient Frontier: Correlation = Return Rik Efficient Frontier: Correlation = Return Rik 9
10 Efficient Frontier: Correlation = Return Rik Efficient Frontier: Correlation = Return Rik 10
11 Efficient Frontier: Correlation = Return Rik The efficient frontier allow u to find the portfolio with maximum return for given rik. The frontier act much like a conumer budget contraint in indicating how the invetor i able to tradeoff rik for return. Jut a the cae of the conumer budget contraint, chooing to be inide the efficient frontier lead to an inefficient outcome. The quetion now i to begin to addre the quetion of how the invetor hould chooe between the efficient portfolio. 4. Illutrating reference for Rik and Return Exactly which efficient portfolio hould an invetor chooe? The anwer will depend upon the invetor particular preference. I the invetor willing to take on more rik in order to gain a higher expected rate of return? The invetor preference can be illutrated with a et of indifference curve. Along any particular indifference curve, the invetor ha the ame amount of utility (or, atifaction). The indifference curve will lope upward. Thi indicate that in order to leave the invetor with the ame utility, the invetor mut be compenated with higher expected rate of return for greater level of rik. A higher indifference curve i alway better. Thi imply demontrate that the invetor will achieve a higher level of utility ince hi/her expected rate of return can be higher for any given level of rik. Alternatively, you may read the indifference curve horizontally a tating a lower rik for any given level of expected return. 11
12 Return Return Increaing utility Young Executive Rik Little Old Lady Rik The figure above preent two type of invetor preference. The indifference curve for the young executive demontrate that he require little additional expected return for taking on more rik. The little old lady on the other hand require a large increae in her expected rate of return for taking on additional rik. We can think of reaon why thee type of invetor view the rikreturn tradeoff in their particular way. The young executive ha a teady income in the form of a alary and a long invetment time horizon, which allow him to view the cot of additional return omewhat mildly. The little old lady on the other hand may not have another ource of income and ha a hort invetment horizon (note, not necearily a hort time left to live, but rather need to be cahing out of ome of her invetment oon). The important general point i that for both type of invetor, they till hope to get on the highet indifference curve poible. A we move up indifference curve, the invetor achieve higher expected rate of return for the ame or, le rik. Thu, the higher indifference curve are uperior regardle of preference. 7 We can now turn to the quetion of which efficient portfolio the invetor hould chooe. The invetor problem i to maximize the expected rate of return and minimize the rik of the portfolio ubject to the available efficient portfolio. Graphically, the invetor i attempting to reach the highet indifference curve poible, given the contraint of the efficient frontier. The optimum riky portfolio for an individual invetor will be given by the point at which the indifference curve (illutrating the invetor preference for the rik/return tradeoff) i jut tangent to the efficiency frontier (illutrating all poible efficient portfolio)  thi i point O on the graph. 7 Throughout we aume invetor are rikavere. It i perfectly poible to treat invetor a rikneutral or even rikloving, but the cot of the complication that arie from thoe aumption would eem to far outweight the benefit for u at thi point. 1
13 Return Rik Although the invetor may like to be on the higher indifference curve, it i imply not poible given the characteritic of the riky aet. On the other ide, any other point on the efficiency frontier reult in a lower indifference curve, thu a lower level of utility. The optimum riky portfolio will be different for invetor with different rikreturn preference hence, different hape of their indifference curve uch a the young executive and little old lady. The next ection demontrate that thi reult may not hold in all cae. 4.3 The Separation Theorem A rikfree aet can be introduced into our portfolio. The important implication of thi introduction may appear urpriing. The firt tak, however, will be to deal with the technical apect. Thi can be done in a quick and dirty way. Reconider the tockbond characteritic of ractice. We can work with the cae of a zero correlation coefficient along with a 50% compoition of tock and bond (the rate of return i 8% and tandard deviation 13.87%, ee the table)  call thi the riky portfolio. Now, uppoe you could buy a rikfree treaury bill paying 5%. A portfolio (call it the complete portfolio ) can be compoed of the rikfree aet (treaury bill) and the riky aet (tock and bond). The deciion concern how much of your total amount (e.g., $100,000) i allocated toward each type of aet. The reulting complete portfolio will have an expected rate of return and tandard deviation. We can illutrate the procedure with a little practice problem. roblem 3. An invetor ha $100,000 to invet. The invetor ha choen to contruct a portfolio containing 5% of a rikfree treaury bill (5% rate of return and zero tandard deviation) and 75% of riky aet. The riky portion of the complete portfolio i compoed of 50% tock (10% expected rate of return and 5% tandard deviation) and 50% bond (6% rate of return and 1% 13
14 tandard deviation). Calculate the expected rate of return and tandard deviation of the complete portfolio. Notice, we have already calculated the expected rate of return and tandard deviation for the riky portfolio. All that thi example require i to ue the previou formula with the two type of aet: rikfree and riky portfolio. {Anwer 3. E ( r ) W E( r ) + W E( r ) = (.75)(8) + (.5)(5) = 7.5% C = f f where ubcript C tand for the Complete portfolio (including the rikfree aet), for the riky portfolio, and f for the rikfree aet. σ C = ( W σ ) + ( W σ ) + W W σ σ ρ = [(.75)(13.87)] And, f + [(.5)(0)] f f f + (.75)(.5)(13.87)(0)(0) = σ C = σ C }}} = = 10.4% The intuition of the analyi can be een with the aid of a graph. We will avoid ome of the technical detail. Eentially, we are forming a linear combination of a rikfree aet and a riky portfolio in order to contruct a complete portfolio. If we began with only the rikfree aet, then  uing our numerical example  the complete portfolio would have a rate of return of 5% and zero tandard deviation (thi i the point on the vertical axi). On the other hand, if the complete portfolio did not contain the rikfree aet, then the expected rate of return would be 8% with a tandard deviation of 13.87%  thi i point Z on the graph (note, thi ha been drawn a the optimum riky portfolio for convenience). y varying the percentage of our total invetment allocated to the rikfree aet and riky portfolio, the expected rate of return and tandard deviation will be given by a traight line between the point on the vertical axi repreenting the rikfree aet and point Z, the riky portfolio. The point X repreent the complete portfolio of ractice 3 where the expected rate of return turn out to be 7.5% with a tandard deviation of 10.4%. 14
15 Return CAL Y 8% X Z 5% 13.87% Rik The capital allocation line (CAL) repreent the complete portfolio for variou allocation between the rikfree aet and riky portfolio. The lope (rie/run) of the CAL i given by the following: E( r ) r f σ 8% 5% = 13.87% =.17 The lope i ometime called the rewardtovariability ratio (or, Sharpe ratio). Thi lope equal the increae in expected return than an invetor can obtain per unit of additional tandard deviation (rik). The portion of the line between the rikfree rate of return and point Z i where the invetor i lending a portion of hi/her total invetment to the default free borrower (i.e., the government). Thi i illutrated by point X. What about the portion of the line beyond point Z. Thi part of the line would reult if the invetor could borrow at the rikfree rate, then purchae more than 100% of hi/her own invetment money into the riky portfolio. Thi i illutrated by point Y. Now of coure, except for the government, an invetor cannot actually borrow at thi rikfree rate. If we wanted more realim, then the CAL will have a kink at point Z indicating the lope of the line get flatter a the interet rate on a loan i greater than the rikfree rate. You can alo think of the portion of the CAL beyond Z a indicating that the invetor i buying on margin till though, the cot of doing o will exceed the rikfree rate. What would have happened if a riky portfolio with a higher expected rate of return and tandard deviation had been choen? For example, uppoe you had choen a riky portfolio compoed of 75% tock and 5% bond. Uing our previou number, the expected rate of return would be 9% with a tandard deviation of 18.99% (thi can be een in the previou table). The lope of the CAL would decline lightly. Thi indicate a lower expected rate of return for an additional unit of rik. You could continue along thi path  chooing variou riky portfolio and drawing the CAL. Which CAL would be bet? The one with the highet lope! Thi will occur when the CAL i jut tangent to the efficient frontier. Thi i the one we have drawn in the 15
16 figure. We have everything needed to tate and apply the eparation theorem. efore doing o, conider the path taken to get to thi point. Imagine that you are an invetment counelor. It i your job to et up a financial portfolio for a client. Your firt tep would be to calculate the expected rate of return and tandard deviation for every poible riky financial aet. The probabilitie aociated with the expected value and variance formula can be determined by (a) looking at the pat price data for each aet, (b) conidering the financial poition (e.g., ue of ome accounting and financial ratio) and propect (e.g., a new CEO, a new product line, competition, etc.), and/or (c) ubjective meaure (e.g., gut feeling). Thi i, of coure, a fairly daunting tak. The econd tep i to form variou combination of the riky aet in order to define the efficient frontier (a fairly eay proce with a good computer). Once thi i done, you could top here with the calculation and attempt to undertand your client peronal preference between expected rate of return (a good thing) and rik (a bad thing). Thi i where you would be attempting to dicover your client particular indifference curve. Having done o, you can advie the client to buy a particular portfolio of financial aet. However, and thi i where the eparation theorem come in, uppoe that you have identified what you conider to be an excellent portfolio an optimum portfolio of riky aet. Would you really want to advie your client to chooe another portfolio imply becaue of their peronal preference for return/rik? Shouldn t there be a way to purchae the excellent portfolio and till meet your client peronal preference? Thi take u to the next tep. The third tep i to find a rikfree aet. The U.S. Treaury ill erve thi role nicely. However, you could chooe omething like a money market mutual account for your client where the rate of return wa lightly higher while the rik remain pretty near zero. Whichever rikfree aet you chooe, you mut now contruct the Capital Allocation Line (CAL). You do thi by combining  in variou amount  the riky portfolio on each point of the efficient frontier with the rikfree aet. Identify the CAL with the highet lope. Thi i the one that give the greatet expected return for each additional unit of rik. It i alo the one that i jut tangent to the efficient frontier. The point  labeled Z  on the efficient frontier that i jut tangent to the CAL i that excellent (or, optimal riky) portfolio. Thi i the riky portfolio that you hould advie all your client to hold regardle of their peronal preference for return/rik. It doen t matter if your client i the little old lady or the young executive. The only difference between the client, reflected in their preference, will be how much of their total invetment to allocate to the rikfree aet and how much to thi optimal riky portfolio. For the little ol lady, you may advie her to have a complete portfolio like point X in the figure. In thi cae, he would be holding ome portion of her wealth in rikfree government Tbill. For the young executive, you might encourage the young invetor  willing to take on even more rik in the hope of higher return  to borrower at the rikfree interet rate in order to purchae more of the optimal riky portfolio than what he/he could buy with their current wealth. Graphically, you are moving the invetor up and to the right along the CAL to a point like Y. ut notice, you are till adviing to buy into only the identified optimal riky portfolio. We have eparated the deciion of which riky 16
17 portfolio to hold from the invetor peronal preference. The preference come in only when deciding how much of the rikfree aet to hold. 4.4 Tobin Development of the Separation Theorem The eparation theorem wa not an attempt to implify the invetor olution to Markowitz MeanVariance Analyi. Rather, Jame Tobin original paper (1958) wa intended to provide a more coherent foundation for Keyne Liquidity reference Theory of the Interet Rate. It will be argued in thi appendix that Keyne formulation of the liquidity preference theory of interet wa extremely weak both, from the perpective of development of hi earlier work in A Treatie on Money and the later development of portfolio theory. Tobin eparation theorem wa tangential to MeanVariance Analyi while directly relating to broader iue within macroeconomic theory and policy Keyne Awkward Money Demand Function {{{need to write but the focu will be on: Difficulty of Monetary olicy to lower the longterm interet rate Inelatic expectation Divergence of opinion re normal rate (price) ortfolio i all or nothing deciion}}} 4.4. The Separation Theorem in Relation to Liquidity reference Tobin conidered the cae in which the government iued two type of financial aet: money and bond. Since the government iue both, the rik of default i the ame and zero. In order to implify matter, Tobin aume that the bond iued by the government i a conol. Why i thi aumption a implification? A conol i a pecial type of bond not actually iued by the U.S. government, but ha been iued by other government and can be approximated with a very long term to maturity (e.g., Diney 100 year bond) which make a et yearly payment. The point i that the bond never mature thu, doe not make a final payment (i.e., facevalue). The price and interet rate of a conol are extremely eay to compute. The preent value of all the future yearly payment reduce to a nice formula. (A.1) C1 C C3 = L = 3 (1 + r) (1 + r) (1 + r) C r Where i the price of the bond, r i the interet rate (or, more pecifically, the yield to maturity), and C the yearly coupon payment. Conol are ueful to aume when firt introducing bond becaue it become abolutely clear that the price of the bond and interet rate on the bond move inverely. We can olve for the interet rate by cromultiplying: 17
18 (A.) C r = Thi i imilar to a dividend yield (D/ where D i the yearly dividend payment, in thi cae an expectation mut be formed, and i the price of the hare). The expected rate of return on the bond i compoed of the interet rate on the bond (A.) and the expectation of a capital gain or lo (g). e e (A.3) g = = 1 The expected rate of return on the bond i therefore written a: (A.4) E( r ) = r + g Auming a martingale probability for the expected price implie that thi i equal to the current price. (A.5) E( ) = e = Thi implie that the expected rate of return from holding the bond will be equal to the interet rate hence, the average value of g i zero. (A.6) E( r ) = r Note, however, that the expected price i being treated a a random variable with mean of zero and a contant tandard deviation (e.g., conider it a a random variable with a normal ditribution thu, you need two piece of information to identify it particular normal curve, the mean and tandard deviation). Thi i important becaue one tend to forget about the capital gain/lo ince it drop out of the expected rate of return calculation but, it play an important role in the ret of the analyi. What about the money aet? We aume for implicity that money i defined in uch a way that it pay zero interet and, of coure, ha no capital gain/lo. efore moving on, conider the different definition of money: M1 (currency + checkable depoit), M (M1 + mall aving account), M3 (M + large aving account). Today, bank do in fact pay interet on checking account and have alway paid it on aving account). Furthermore, Keyne had argued that in ome circumtance money hould be defined to include hortterm government Treaury bill. For Keyne, the eential difference between money and bond wa their price fluctuation. The price of a hortterm Tbill will not fluctuate very much with a change in the interet rate. On the other hand, the price of a longterm government bond (uch a a conol) would fluctuate greatly with a change in the interet rate. In modern terminology, the percentage change in the price brought about by a one percent change in the interet rate i called the duration. The difference between money and bond, for Keyne, amount to the notion that 18
19 duration i mall for money and large for bond. For u, thi amount to auming that the capital gain/lo on money i negligible hence, the variance of thi i o low that it can be afely ignored. Thu, money ha a zero expected rate of return and variance hould be a afe aumption we can alway define the money aet o that it ha the characteritic, or very cloe. At thi point, we can apply the tool developed to handle the MeanVariance Analyi. The expected rate of return on the portfolio i merely a weighted average of the expected return for the individual aet. (A.7) E( r ) = W E( r M E( r ) = r E( r ) = W r M ) = 0, E( r M ) + W E( r ) The variance of the portfolio i not the imple weighted average of the individual aet variance. We have een that thi depend upon the covariance (hence, correlation) between the aet. σ = ( W σ ) + ( W σ ) + ( W σ )( W σ ) ρ M M M M Thi implifie greatly once we recall that the rate of return on the money aet ha zero variance. Hence, we get the following. (A.8) σ = ( W σ ) The tandard deviation (i.e., rik) of the portfolio i imply the quare root of the variance. (A.9) σ = W σ All of thi ha been accomplihed with the tool ued in contructing the efficient frontier. The difference i that we have introduced an aet without rik and return what i called a rikfree aet. The introduction of thi type of aet carrie greater ignificance than what one might expect. In the preent context, our goal i to contruct the demand chedule for the rikfree aet. The available tradeoff between rik and return can be developed from equation (A.7) and (A.9). Thi tradeoff will be given by the lope of the line depicting the relationhip between rik and return on the portfolio. (A.10) r E( r ) = σ σ Notice, thi line i derived for olving (A.7) and (A.9) for the proportion of the portfolio held in bond and equating the reult. Graphically, the line i depicted in Figure A.1. 19
20 E(r) Figure A.1 Rik of ortfolio Notice, the line will tilt upward for an increae in the interet rate on bond or a decreae in the rik of the bond. The pecific place an invetor will chooe will depend upon how they view the rik and return tradeoff. Since it depend upon their ubjective preference for rik and return we can depict their willingne in term of indifference curve a done previouly. In order to tranlate the deciion concerning rik and return into the reulting proportion of bond and money held we imply rearrange equation (A.9). (A.11) W σ = σ Recall, the proportion of money held in the portfolio will be given by one minu the proportion of bond held. Thi relationhip i graphed in Figure A.. 0
21 Wb Figure A. Rik of ortfolio We can now put everything together to derive a money demand chedule baed on portfolio choice (of the MeanVariance variety). Figure A.3 depict the reult. Notice, the demand for money i read upward on the lower quadrant. Thu, a the interet rate increae, the top line will tilt upward normally leading to an increae in the proportion of bond held and decreae in the proportion of money normally i conditional upon how invetor for rik, i.e., their indifference curve. We, therefore, derive the demand for money chedule by allowing the interet rate to vary. If the rik of bond decline, the upper line tilt upward again and the lower line tilt downward! 1
22 E(r) Sigmabond Rik of ortfolio 1 percentage of wealth held in the form of money Wb Figure A.3
MBA 570x Homework 1 Due 9/24/2014 Solution
MA 570x Homework 1 Due 9/24/2014 olution Individual work: 1. Quetion related to Chapter 11, T Why do you think i a fund of fund market for hedge fund, but not for mutual fund? Anwer: Invetor can inexpenively
More informationMSc Financial Economics: International Finance. Bubbles in the Foreign Exchange Market. Anne Sibert. Revised Spring 2013. Contents
MSc Financial Economic: International Finance Bubble in the Foreign Exchange Market Anne Sibert Revied Spring 203 Content Introduction................................................. 2 The Mone Market.............................................
More informationUnit 11 Using Linear Regression to Describe Relationships
Unit 11 Uing Linear Regreion to Decribe Relationhip Objective: To obtain and interpret the lope and intercept of the leat quare line for predicting a quantitative repone variable from a quantitative explanatory
More informationProject Management Basics
Project Management Baic A Guide to undertanding the baic component of effective project management and the key to ucce 1 Content 1.0 Who hould read thi Guide... 3 1.1 Overview... 3 1.2 Project Management
More informationA technical guide to 2014 key stage 2 to key stage 4 value added measures
A technical guide to 2014 key tage 2 to key tage 4 value added meaure CONTENTS Introduction: PAGE NO. What i value added? 2 Change to value added methodology in 2014 4 Interpretation: Interpreting chool
More informationQueueing systems with scheduled arrivals, i.e., appointment systems, are typical for frontal service systems,
MANAGEMENT SCIENCE Vol. 54, No. 3, March 28, pp. 565 572 in 25199 ein 1526551 8 543 565 inform doi 1.1287/mnc.17.82 28 INFORMS Scheduling Arrival to Queue: A SingleServer Model with NoShow INFORMS
More informationMorningstar Fixed Income Style Box TM Methodology
Morningtar Fixed Income Style Box TM Methodology Morningtar Methodology Paper Augut 3, 00 00 Morningtar, Inc. All right reerved. The information in thi document i the property of Morningtar, Inc. Reproduction
More informationv = x t = x 2 x 1 t 2 t 1 The average speed of the particle is absolute value of the average velocity and is given Distance travelled t
Chapter 2 Motion in One Dimenion 2.1 The Important Stuff 2.1.1 Poition, Time and Diplacement We begin our tudy of motion by conidering object which are very mall in comparion to the ize of their movement
More informationQuadrilaterals. Learning Objectives. PreActivity
Section 3.4 PreActivity Preparation Quadrilateral Intereting geometric hape and pattern are all around u when we tart looking for them. Examine a row of fencing or the tiling deign at the wimming pool.
More informationMorningstar FixedIncome Style Box TM Methodology
Morningtar FixedIncome Style Box TM Methodology Morningtar Methodology Paper April 30, 01 01 Morningtar, Inc. All right reerved. The information in thi document i the property of Morningtar, Inc. Reproduction
More informationChapter 10 Stocks and Their Valuation ANSWERS TO ENDOFCHAPTER QUESTIONS
Chapter Stoc and Their Valuation ANSWERS TO ENOFCHAPTER QUESTIONS  a. A proxy i a document giving one peron the authority to act for another, typically the power to vote hare of common toc. If earning
More informationSenior Thesis. Horse Play. Optimal Wagers and the Kelly Criterion. Author: Courtney Kempton. Supervisor: Professor Jim Morrow
Senior Thei Hore Play Optimal Wager and the Kelly Criterion Author: Courtney Kempton Supervior: Profeor Jim Morrow June 7, 20 Introduction The fundamental problem in gambling i to find betting opportunitie
More informationNewton s Laws. A force is simply a push or a pull. Forces are vectors; they have both size and direction.
Newton Law Newton firt law: An object will tay at ret or in a tate of uniform motion with contant velocity, in a traight line, unle acted upon by an external force. In other word, the bodie reit any change
More informationnaifa Members: SERVING AMERICA S NEIGHBORHOODS FOR 120 YEARS
naifa Member: SERVING AMERICA S NEIGHBORHOODS FOR 120 YEARS National Aociation of Inurance and Financial Advior Serving America Neigborhood for Over 120 Year Since 1890, NAIFA ha worked to afeguard the
More informationReview of Multiple Regression Richard Williams, University of Notre Dame, http://www3.nd.edu/~rwilliam/ Last revised January 13, 2015
Review of Multiple Regreion Richard William, Univerity of Notre Dame, http://www3.nd.edu/~rwilliam/ Lat revied January 13, 015 Aumption about prior nowledge. Thi handout attempt to ummarize and yntheize
More informationMECH 2110  Statics & Dynamics
Chapter D Problem 3 Solution 1/7/8 1:8 PM MECH 11  Static & Dynamic Chapter D Problem 3 Solution Page 7, Engineering Mechanic  Dynamic, 4th Edition, Meriam and Kraige Given: Particle moving along a traight
More informationProfitability of Loyalty Programs in the Presence of Uncertainty in Customers Valuations
Proceeding of the 0 Indutrial Engineering Reearch Conference T. Doolen and E. Van Aken, ed. Profitability of Loyalty Program in the Preence of Uncertainty in Cutomer Valuation Amir Gandomi and Saeed Zolfaghari
More informationChapter 32. OPTICAL IMAGES 32.1 Mirrors
Chapter 32 OPTICAL IMAGES 32.1 Mirror The point P i called the image or the virtual image of P (light doe not emanate from it) The leftright reveral in the mirror i alo called the depth inverion (the
More informationA note on profit maximization and monotonicity for inbound call centers
A note on profit maximization and monotonicity for inbound call center Ger Koole & Aue Pot Department of Mathematic, Vrije Univeriteit Amterdam, The Netherland 23rd December 2005 Abtract We conider an
More informationFinite Automata. a) Reading a symbol, b) Transferring to a new instruction, and c) Advancing the tape head one square to the right.
Finite Automata Let u begin by removing almot all of the Turing machine' power! Maybe then we hall have olvable deciion problem and till be able to accomplih ome computational tak. Alo, we might be able
More information12.4 Problems. Excerpt from "Introduction to Geometry" 2014 AoPS Inc. Copyrighted Material CHAPTER 12. CIRCLES AND ANGLES
HTER 1. IRLES N NGLES Excerpt from "Introduction to Geometry" 014 os Inc. onider the circle with diameter O. all thi circle. Why mut hit O in at leat two di erent point? (b) Why i it impoible for to hit
More informationGlobal Imbalances or Bad Accounting? The Missing Dark Matter in the Wealth of Nations. Ricardo Hausmann and Federico Sturzenegger
Global Imbalance or Bad Accounting? The Miing Dark Matter in the Wealth of Nation Ricardo Haumann and Federico Sturzenegger CID Working Paper No. 124 January 2006 Copyright 2006 Ricardo Haumann, Federico
More informationFEDERATION OF ARAB SCIENTIFIC RESEARCH COUNCILS
Aignment Report RP/98983/5/0./03 Etablihment of cientific and technological information ervice for economic and ocial development FOR INTERNAL UE NOT FOR GENERAL DITRIBUTION FEDERATION OF ARAB CIENTIFIC
More informationAssessing the Discriminatory Power of Credit Scores
Aeing the Dicriminatory Power of Credit Score Holger Kraft 1, Gerald Kroiandt 1, Marlene Müller 1,2 1 Fraunhofer Intitut für Techno und Wirtchaftmathematik (ITWM) GottliebDaimlerStr. 49, 67663 Kaierlautern,
More informationRISK MANAGEMENT POLICY
RISK MANAGEMENT POLICY The practice of foreign exchange (FX) rik management i an area thrut into the potlight due to the market volatility that ha prevailed for ome time. A a conequence, many corporation
More informationOffice of Tax Analysis U.S. Department of the Treasury. A Dynamic Analysis of Permanent Extension of the President s Tax Relief
Office of Tax Analyi U.S. Department of the Treaury A Dynamic Analyi of Permanent Extenion of the Preident Tax Relief July 25, 2006 Executive Summary Thi Report preent a detailed decription of Treaury
More informationA Note on Profit Maximization and Monotonicity for Inbound Call Centers
OPERATIONS RESEARCH Vol. 59, No. 5, September October 2011, pp. 1304 1308 in 0030364X ein 15265463 11 5905 1304 http://dx.doi.org/10.1287/opre.1110.0990 2011 INFORMS TECHNICAL NOTE INFORMS hold copyright
More informationOptical Illusion. Sara Bolouki, Roger Grosse, Honglak Lee, Andrew Ng
Optical Illuion Sara Bolouki, Roger Groe, Honglak Lee, Andrew Ng. Introduction The goal of thi proect i to explain ome of the illuory phenomena uing pare coding and whitening model. Intead of the pare
More informationCASE STUDY BRIDGE. www.futureprocessing.com
CASE STUDY BRIDGE TABLE OF CONTENTS #1 ABOUT THE CLIENT 3 #2 ABOUT THE PROJECT 4 #3 OUR ROLE 5 #4 RESULT OF OUR COLLABORATION 67 #5 THE BUSINESS PROBLEM THAT WE SOLVED 8 #6 CHALLENGES 9 #7 VISUAL IDENTIFICATION
More information6. Friction, Experiment and Theory
6. Friction, Experiment and Theory The lab thi wee invetigate the rictional orce and the phyical interpretation o the coeicient o riction. We will mae ue o the concept o the orce o gravity, the normal
More informationThe Cash Flow Statement: Problems with the Current Rules
A C C O U N T I N G & A U D I T I N G accounting The Cah Flow Statement: Problem with the Current Rule By Neii S. Wei and Jame G.S. Yang In recent year, the tatement of cah flow ha received increaing attention
More informationIs MarktoMarket Accounting Destabilizing? Analysis and Implications for Policy
Firt draft: 4/12/2008 I MarktoMarket Accounting Detabilizing? Analyi and Implication for Policy John Heaton 1, Deborah Luca 2 Robert McDonald 3 Prepared for the Carnegie Rocheter Conference on Public
More informationTwo Dimensional FEM Simulation of Ultrasonic Wave Propagation in Isotropic Solid Media using COMSOL
Excerpt from the Proceeding of the COMSO Conference 0 India Two Dimenional FEM Simulation of Ultraonic Wave Propagation in Iotropic Solid Media uing COMSO Bikah Ghoe *, Krihnan Balaubramaniam *, C V Krihnamurthy
More informationCHARACTERISTICS OF WAITING LINE MODELS THE INDICATORS OF THE CUSTOMER FLOW MANAGEMENT SYSTEMS EFFICIENCY
Annale Univeritati Apuleni Serie Oeconomica, 2(2), 200 CHARACTERISTICS OF WAITING LINE MODELS THE INDICATORS OF THE CUSTOMER FLOW MANAGEMENT SYSTEMS EFFICIENCY Sidonia Otilia Cernea Mihaela Jaradat 2 Mohammad
More informationGrowth and Sustainability of Managed Security Services Networks: An Economic Perspective
Growth and Sutainability of Managed Security Service etwork: An Economic Perpective Alok Gupta Dmitry Zhdanov Department of Information and Deciion Science Univerity of Minneota Minneapoli, M 55455 (agupta,
More informationBidding for Representative Allocations for Display Advertising
Bidding for Repreentative Allocation for Diplay Advertiing Arpita Ghoh, Preton McAfee, Kihore Papineni, and Sergei Vailvitkii Yahoo! Reearch. {arpita, mcafee, kpapi, ergei}@yahooinc.com Abtract. Diplay
More informationCASE STUDY ALLOCATE SOFTWARE
CASE STUDY ALLOCATE SOFTWARE allocate caetud y TABLE OF CONTENTS #1 ABOUT THE CLIENT #2 OUR ROLE #3 EFFECTS OF OUR COOPERATION #4 BUSINESS PROBLEM THAT WE SOLVED #5 CHALLENGES #6 WORKING IN SCRUM #7 WHAT
More information2. METHOD DATA COLLECTION
Key to learning in pecific ubject area of engineering education an example from electrical engineering AnnaKarin Cartenen,, and Jonte Bernhard, School of Engineering, Jönköping Univerity, S Jönköping,
More informationOhm s Law. Ohmic relationship V=IR. Electric Power. Non Ohmic devises. Schematic representation. Electric Power
Ohm Law Ohmic relationhip V=IR Ohm law tate that current through the conductor i directly proportional to the voltage acro it if temperature and other phyical condition do not change. In many material,
More informationSample Problems Chapter 9
Sample roblem Chapter 9 Title: referred tock (olve for value) 1. Timele Corporation iued preferred tock with a par value of $7. The tock promied to pay an annual dividend equal to 19.% of the par value.
More informationSoftware Engineering Management: strategic choices in a new decade
Software Engineering : trategic choice in a new decade Barbara Farbey & Anthony Finkeltein Univerity College London, Department of Computer Science, Gower St. London WC1E 6BT, UK {b.farbey a.finkeltein}@ucl.ac.uk
More informationMixed Method of Model Reduction for Uncertain Systems
SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol 4 No June Mixed Method of Model Reduction for Uncertain Sytem N Selvaganean Abtract: A mixed method for reducing a higher order uncertain ytem to a table reduced
More informationThus far. Inferences When Comparing Two Means. Testing differences between two means or proportions
Inference When Comparing Two Mean Dr. Tom Ilvento FREC 48 Thu far We have made an inference from a ingle ample mean and proportion to a population, uing The ample mean (or proportion) The ample tandard
More informationPOSSIBILITIES OF INDIVIDUAL CLAIM RESERVE RISK MODELING
POSSIBILITIES OF INDIVIDUAL CLAIM RESERVE RISK MODELING Pavel Zimmermann * 1. Introduction A ignificant increae in demand for inurance and financial rik quantification ha occurred recently due to the fact
More informationREDUCTION OF TOTAL SUPPLY CHAIN CYCLE TIME IN INTERNAL BUSINESS PROCESS OF REAMER USING DOE AND TAGUCHI METHODOLOGY. Abstract. 1.
International Journal of Advanced Technology & Engineering Reearch (IJATER) REDUCTION OF TOTAL SUPPLY CHAIN CYCLE TIME IN INTERNAL BUSINESS PROCESS OF REAMER USING DOE AND Abtract TAGUCHI METHODOLOGY Mr.
More informationHUMAN CAPITAL AND THE FUTURE OF TRANSITION ECONOMIES * Michael Spagat Royal Holloway, University of London, CEPR and Davidson Institute.
HUMAN CAPITAL AND THE FUTURE OF TRANSITION ECONOMIES * By Michael Spagat Royal Holloway, Univerity of London, CEPR and Davidon Intitute Abtract Tranition economie have an initial condition of high human
More informationAuction Theory. Jonathan Levin. October 2004
Auction Theory Jonathan Levin October 2004 Our next topic i auction. Our objective will be to cover a few of the main idea and highlight. Auction theory can be approached from different angle from the
More informationTIME SERIES ANALYSIS AND TRENDS BY USING SPSS PROGRAMME
TIME SERIES ANALYSIS AND TRENDS BY USING SPSS PROGRAMME RADMILA KOCURKOVÁ Sileian Univerity in Opava School of Buine Adminitration in Karviná Department of Mathematical Method in Economic Czech Republic
More informationLinear Momentum and Collisions
Chapter 7 Linear Momentum and Colliion 7.1 The Important Stuff 7.1.1 Linear Momentum The linear momentum of a particle with ma m moving with velocity v i defined a p = mv (7.1) Linear momentum i a vector.
More informationQueueing Models for Multiclass Call Centers with RealTime Anticipated Delays
Queueing Model for Multicla Call Center with RealTime Anticipated Delay Oualid Jouini Yve Dallery Zeynep Akşin Ecole Centrale Pari Koç Univerity Laboratoire Génie Indutriel College of Adminitrative Science
More informationNew Sales Productivity
EBOOK New Sale Productivity Help ale rookie get off the bench and into the game Sponored by Table of Content Introduction 3 4 5 6 8 9 About SAVO 10 NewHire Ramping 2 Introduction A new hire can t tranform
More informationA Life Contingency Approach for Physical Assets: Create Volatility to Create Value
A Life Contingency Approach for Phyical Aet: Create Volatility to Create Value homa Emil Wendling 2011 Enterprie Rik Management Sympoium Society of Actuarie March 1416, 2011 Copyright 2011 by the Society
More informationGrowth and Sustainability of Managed Security Services Networks: An Economic Perspective
Growth and Sutainability of Managed Security Service etwork: An Economic Perpective Alok Gupta Dmitry Zhdanov Department of Information and Deciion Science Univerity of Minneota Minneapoli, M 55455 (agupta,
More informationRisk Management for a Global Supply Chain Planning under Uncertainty: Models and Algorithms
Rik Management for a Global Supply Chain Planning under Uncertainty: Model and Algorithm Fengqi You 1, John M. Waick 2, Ignacio E. Gromann 1* 1 Dept. of Chemical Engineering, Carnegie Mellon Univerity,
More informationA Spam Message Filtering Method: focus on run time
, pp.2933 http://dx.doi.org/10.14257/atl.2014.76.08 A Spam Meage Filtering Method: focu on run time SinEon Kim 1, JungTae Jo 2, SangHyun Choi 3 1 Department of Information Security Management 2 Department
More informationChapter 10 Velocity, Acceleration, and Calculus
Chapter 10 Velocity, Acceleration, and Calculu The firt derivative of poition i velocity, and the econd derivative i acceleration. Thee derivative can be viewed in four way: phyically, numerically, ymbolically,
More informationBiObjective Optimization for the Clinical Trial Supply Chain Management
Ian David Lockhart Bogle and Michael Fairweather (Editor), Proceeding of the 22nd European Sympoium on Computer Aided Proce Engineering, 1720 June 2012, London. 2012 Elevier B.V. All right reerved. BiObjective
More informationPartial optimal labeling search for a NPhard subclass of (max,+) problems
Partial optimal labeling earch for a NPhard ubcla of (max,+) problem Ivan Kovtun International Reearch and Training Center of Information Technologie and Sytem, Kiev, Uraine, ovtun@image.iev.ua Dreden
More informationSolution of the Heat Equation for transient conduction by LaPlace Transform
Solution of the Heat Equation for tranient conduction by LaPlace Tranform Thi notebook ha been written in Mathematica by Mark J. McCready Profeor and Chair of Chemical Engineering Univerity of Notre Dame
More informationDISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENTMATCHING INTRUSION DETECTION SYSTEMS
DISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENTMATCHING INTRUSION DETECTION SYSTEMS Chritopher V. Kopek Department of Computer Science Wake Foret Univerity WintonSalem, NC, 2709 Email: kopekcv@gmail.com
More informationUnusual Option Market Activity and the Terrorist Attacks of September 11, 2001*
Allen M. Potehman Univerity of Illinoi at UrbanaChampaign Unuual Option Market Activity and the Terrorit Attack of September 11, 2001* I. Introduction In the aftermath of the terrorit attack on the World
More informationSolution: The optimal position for an investor with a coefficient of risk aversion A = 5 in the risky asset is y*:
Problem 1. Consider a risky asset. Suppose the expected rate of return on the risky asset is 15%, the standard deviation of the asset return is 22%, and the riskfree rate is 6%. What is your optimal position
More informationDISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENTMATCHING INTRUSION DETECTION SYSTEMS. G. Chapman J. Cleese E. Idle
DISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENTMATCHING INTRUSION DETECTION SYSTEMS G. Chapman J. Cleee E. Idle ABSTRACT Content matching i a neceary component of any ignaturebaed network Intruion Detection
More informationCorporate Tax Aggressiveness and the Role of Debt
Corporate Tax Aggreivene and the Role of Debt Akankha Jalan, Jayant R. Kale, and Cotanza Meneghetti Abtract We examine the effect of leverage on corporate tax aggreivene. We derive the optimal level of
More informationJanuary 21, 2015. Abstract
T S U I I E P : T R M C S J. R January 21, 2015 Abtract Thi paper evaluate the trategic behavior of a monopolit to influence environmental policy, either with taxe or with tandard, comparing two alternative
More information1 Introduction. Reza Shokri* Privacy Games: Optimal UserCentric Data Obfuscation
Proceeding on Privacy Enhancing Technologie 2015; 2015 (2):1 17 Reza Shokri* Privacy Game: Optimal UerCentric Data Obfucation Abtract: Conider uer who hare their data (e.g., location) with an untruted
More informationProgress 8 measure in 2016, 2017, and 2018. Guide for maintained secondary schools, academies and free schools
Progre 8 meaure in 2016, 2017, and 2018 Guide for maintained econdary chool, academie and free chool July 2016 Content Table of figure 4 Summary 5 A ummary of Attainment 8 and Progre 8 5 Expiry or review
More informationBuying High and Selling Low: Stock Repurchases and Persistent Asymmetric Information
RFS Advance Acce publihed February 9, 06 Buying High and Selling Low: Stock Repurchae and Peritent Aymmetric Information Philip Bond Univerity of Wahington Hongda Zhong London School of Economic Share
More informationMassachusetts Institute of Technology Department of Electrical Engineering and Computer Science
aachuett Intitute of Technology Department of Electrical Engineering and Computer Science 6.685 Electric achinery Cla Note 10: Induction achine Control and Simulation c 2003 Jame L. Kirtley Jr. 1 Introduction
More informationTRADING rules are widely used in financial market as
Complex Stock Trading Strategy Baed on Particle Swarm Optimization Fei Wang, Philip L.H. Yu and David W. Cheung Abtract Trading rule have been utilized in the tock market to make profit for more than a
More informationShortterm allocation of gas networks and gaselectricity input foreclosure
Shortterm allocation of ga network and gaelectricity input forecloure Miguel Vazquez a,, Michelle Hallack b a Economic Intitute (IE), Federal Univerity of Rio de Janeiro (UFRJ) b Economic Department,
More informationSection 5.2  Random Variables
MAT 0  Introduction to Statitic Section 5.  Random Variable A random variable i a variable that take on different numerical value which are determined by chance. Example 5. pg. 33 For each random experiment,
More informationStochastic House Appreciation and Optimal Mortgage Lending
Stochatic Houe Appreciation and Optimal Mortgage Lending Tomaz Pikorki Columbia Buine School tp2252@columbia.edu Alexei Tchityi UC Berkeley Haa tchityi@haa.berkeley.edu December 28 Abtract We characterize
More informationUnobserved Heterogeneity and Risk in Wage Variance: Does Schooling Provide Earnings Insurance?
TI 011045/3 Tinbergen Intitute Dicuion Paper Unoberved Heterogeneity and Rik in Wage Variance: Doe Schooling Provide Earning Inurance? Jacopo Mazza Han van Ophem Joop Hartog * Univerity of Amterdam; *
More informationTHE IMPACT OF MULTIFACTORIAL GENETIC DISORDERS ON CRITICAL ILLNESS INSURANCE: A SIMULATION STUDY BASED ON UK BIOBANK ABSTRACT KEYWORDS
THE IMPACT OF MULTIFACTORIAL GENETIC DISORDERS ON CRITICAL ILLNESS INSURANCE: A SIMULATION STUDY BASED ON UK BIOBANK BY ANGUS MACDONALD, DELME PRITCHARD AND PRADIP TAPADAR ABSTRACT The UK Biobank project
More informationCHAPTER 7: OPTIMAL RISKY PORTFOLIOS
CHAPTER 7: OPTIMAL RIKY PORTFOLIO PROLEM ET 1. (a) and (e).. (a) and (c). After real estate is added to the portfolio, there are four asset classes in the portfolio: stocks, bonds, cash and real estate.
More informationControl of Wireless Networks with Flow Level Dynamics under Constant Time Scheduling
Control of Wirele Network with Flow Level Dynamic under Contant Time Scheduling Long Le and Ravi R. Mazumdar Department of Electrical and Computer Engineering Univerity of Waterloo,Waterloo, ON, Canada
More informationTtest for dependent Samples. Difference Scores. The t Test for Dependent Samples. The t Test for Dependent Samples. s D
The t Tet for ependent Sample Ttet for dependent Sample (ak.a., Paired ample ttet, Correlated Group eign, Within Subject eign, Repeated Meaure,.. RepeatedMeaure eign When you have two et of core from
More informationStochastic House Appreciation and Optimal Subprime Lending
Stochatic Houe Appreciation and Optimal Subprime Lending Tomaz Pikorki Columbia Buine School tp5@mail.gb.columbia.edu Alexei Tchityi NYU Stern atchity@tern.nyu.edu February 8 Abtract Thi paper tudie an
More informationIMPORTANT: Read page 2 ASAP. *Please feel free to email (longo.physics@gmail.com) me at any time if you have questions or concerns.
rev. 05/4/16 AP Phyic C: Mechanic Summer Aignment 016017 Mr. Longo Foret Park HS longo.phyic@gmail.com longodb@pwc.edu Welcome to AP Phyic C: Mechanic. The purpoe of thi ummer aignment i to give you a
More informationSector Concentration in Loan Portfolios and Economic Capital. Abstract
Sector Concentration in Loan Portfolio and Economic Capital Klau Düllmann and Nancy Machelein 2 Thi verion: September 2006 Abtract The purpoe of thi paper i to meaure the potential impact of buineector
More informationSCM integration: organiational, managerial and technological iue M. Caridi 1 and A. Sianei 2 Dipartimento di Economia e Produzione, Politecnico di Milano, Italy Email: maria.caridi@polimi.it Itituto
More informationScheduling of Jobs and Maintenance Activities on Parallel Machines
Scheduling of Job and Maintenance Activitie on Parallel Machine ChungYee Lee* Department of Indutrial Engineering Texa A&M Univerity College Station, TX 778433131 cylee@ac.tamu.edu ZhiLong Chen** Department
More informationFree Enterprise, the Economy and Monetary Policy
Free Enterprie, the Economy and Monetary Policy free (fre) adj. not cont Free enterprie i the freedom of individual and buinee to power of another; at regulation. It enable individual and buinee to create,
More informationA Resolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networks
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Joé Craveirinha a,c, Rita GirãoSilva a,c, João Clímaco b,c, Lúcia Martin a,c a b c DEECFCTUC FEUC INESCCoimbra International
More informationINFORMATION Technology (IT) infrastructure management
IEEE TRANSACTIONS ON CLOUD COMPUTING, VOL. 2, NO. 1, MAY 214 1 BuineDriven Longterm Capacity Planning for SaaS Application David Candeia, Ricardo Araújo Santo and Raquel Lope Abtract Capacity Planning
More informationCapital Investment. Decisions: An Overview Appendix. Introduction. Analyzing Cash Flows for Present Value Analysis
f. Capital Invetment Deciion: An Overview Appendix Introduction Capital invetment deciion are the reponibility of manager of invetment center (ee Chapter 12). The analyi of capital invetment deciion i
More informationHealth Insurance and Social Welfare. Run Liang. China Center for Economic Research, Peking University, Beijing 100871, China,
Health Inurance and Social Welfare Run Liang China Center for Economic Reearch, Peking Univerity, Beijing 100871, China, Email: rliang@ccer.edu.cn and Hao Wang China Center for Economic Reearch, Peking
More informationMULTIOBJECTIVE APPROACHES TO PUBLIC DEBT MANAGEMENT
MULTIOBJECTIVE APPROACHES TO PUBLIC DEBT MANAGEMENT A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SC IENCES OF MIDDLE EAST TECHNICAL UNIVERSITY BY EMRE BALIBEK IN PARTIAL FULFILLMENT
More informationPEM GROUP 2015 FINANCIAL RESULTS
Venture Debt Fund July 2015 PEM GROUP 2015 FINANCIAL RESULTS WARSAW, 10 MARCH 2016 Agenda Key miletone in 2015 TSR  our offer for invetor 2015 financial reult Lat 4 year in number New invetment in 2015
More informationSupport Vector Machine Based Electricity Price Forecasting For Electricity Markets utilising Projected Assessment of System Adequacy Data.
The Sixth International Power Engineering Conference (IPEC23, 2729 November 23, Singapore Support Vector Machine Baed Electricity Price Forecating For Electricity Maret utiliing Projected Aement of Sytem
More informationBrokerage Commissions and Institutional Trading Patterns
rokerage Commiion and Intitutional Trading Pattern Michael Goldtein abon College Paul Irvine Emory Univerity Eugene Kandel Hebrew Univerity and Zvi Wiener Hebrew Univerity June 00 btract Why do broker
More informationPATENT SETTLEMENT AGREEMENTS
Chapter 85 ATNT STTLMNT AGRMNTS Sumanth Addanki and Alan J. akin * Variou commentator have argued that while agreement in ettlement of patent litigation are generally procompetitive, they can harm conumer
More informationName: SID: Instructions
CS168 Fall 2014 Homework 1 Aigned: Wedneday, 10 September 2014 Due: Monday, 22 September 2014 Name: SID: Dicuion Section (Day/Time): Intruction  Submit thi homework uing Pandagrader/GradeScope(http://www.gradecope.com/
More informationIntroduction to the article Degrees of Freedom.
Introduction to the article Degree of Freedom. The article by Walker, H. W. Degree of Freedom. Journal of Educational Pychology. 3(4) (940) 5369, wa trancribed from the original by Chri Olen, George Wahington
More informationRedesigning Ratings: Assessing the Discriminatory Power of Credit Scores under Censoring
Redeigning Rating: Aeing the Dicriminatory Power of Credit Score under Cenoring Holger Kraft, Gerald Kroiandt, Marlene Müller Fraunhofer Intitut für Techno und Wirtchaftmathematik (ITWM) Thi verion: June
More informationProgress 8 and Attainment 8 measure in 2016, 2017, and 2018. Guide for maintained secondary schools, academies and free schools
Progre 8 and Attainment 8 meaure in 2016, 2017, and 2018 Guide for maintained econdary chool, academie and free chool September 2016 Content Table of figure 4 Summary 5 A ummary of Attainment 8 and Progre
More informationProceedings of Power Tech 2007, July 15, Lausanne
Second Order Stochatic Dominance Portfolio Optimization for an Electric Energy Company M.P. Cheong, Student Member, IEEE, G. B. Sheble, Fellow, IEEE, D. Berleant, Senior Member, IEEE and C.C. Teoh, Student
More informationPiracy in twosided markets
Technical Workhop on the Economic of Regulation Piracy in twoided market Paul Belleflamme, CORE & LSM Univerité catholique de Louvain 07/12/2011 OECD, Pari Outline Piracy in oneided market o Baic model
More informationINSIDE REPUTATION BULLETIN
email@inidetory.com.au www.inidetory.com.au +61 (2) 9299 9979 The reputational impact of outourcing overea The global financial crii ha reulted in extra preure on Autralian buinee to tighten their belt.
More information