Real Estate Equity Derivatives
|
|
- Jason Hunt
- 8 years ago
- Views:
Transcription
1 Real Estate Equity Deivatives Geltne Mille 2 nd Edition Chapte 26 Section 26.3 Real Estate Deivatives (Index Retun Swaps)
2 Real Estate Equity Deivatives A deivative is an asset whose value depends completely on the value o anothe asset (o a combination o assets). e.g., Stock options. Cuently, pivate equity R.E. deivatives oeed ae essentially utues contacts: No cash changes hands up ont ( notional tade amt. ) The majo poducts ae swaps : e.g., Swap NPI etun o a ixed etun each quate.
3 Poducts Cuently Oeed NPI Appeciation Swap o Fixed NPI Total Retun Swap o Fixed NPI Popety Type Total Retun Swap Simila poducts on IPD in U.K.
4 How Deivatives Wok: An Example... Littleton Fieman s Fund is a Pension Fund that wants to invest in diect (pivate) eal estate o potolio divesiication But Littleton is small: They ace high tansaction costs and/o low divesiication within eal estate (ew popeties: noise, basis isk ); and Littleton is woied about lack o pivate R.E. liquidity (0 yea investment?!?...) Southen State Teaches is a lage pension und, aleady invested in eal estate. Southen inds itsel ove-invested in R.E. due to denominato eect (stock mkt decline puts them ove-taget in R.E.). Southen hates to sell any o thei individual popeties because they like these popeties and they hate to incu the high tansactions cost o sale; but They need to educe thei exposue to the R.E. asset class in thei potolio.
5 How Deivatives Wok: An Example... Both paties can beneit om the NCREIF Appeciation Swap: Littleton takes the long position (swaps ixed etun o NPI appeciation etun). Southen takes the shot position (swaps NPI appeciation etun o the ixed etun). Southen pays Littleton (shot pays long) the NPI appeciation etun ( loating leg ) on the notional tade amount each quate. Littleton pays Southen (long pays shot) the ixed leg (spead) on the notional tade amount each quate. Net cash owed is settled at the end o each quate when the NPI is epoted, o duation o swap contact (typically 2-3 yeas).
6 Suppose Littleton & Southen agee on a two yea contact to tade a notional amount o $00 million at the end o 2005, with a ixed leg (spead) o 00bps: No cash changes hands at end o 2005Q4. Suppose 2006Q NPI appeciation etun is 2.5%, then: Southen owes Littleton (shot owes long).025*$00 = $2,500,000; Littleton owes Southen (long owes shot).0*$00 = $,000,000; They settle net cash low: Southen pays Littleton $,500,000. Suppose 2006Q2 NPI appeciation etun is then negative.0%: Southen owes Littleton -.0*$00 = -$,000,000 (i.e., Littleton owes Southen $,000,000); Littleton still owes Southen anothe $,000,000 on the ixed spead (as always); They settle net cash low: Littleton pays southen $2,000,000. This pocess continues though 2007Q4. How Deivatives Wok: An Example...
7 How Deivatives Wok: An Example... Potolio isk impact on Littleton (long position): Gains isk eect o $00 million woth o eal estate investment; Loses isk eect o $00 million woth o iskee bond investment. i.e.: They ve swapped $00 million o iskee bond isk o $00 million o pivate R.E. isk (because vitually all o the quately isk in R.E. investment is in the appeciation etun).
8 How Deivatives Wok: An Example... Potolio isk impact on Southen (shot position): Gains isk eect o $00 million woth o iskee bonds; Loses isk eect o $00 million woth o pivate R.E. investment (like NPI). i.e.: They ve swapped $00 million o eal estate isk o $00 million o iskee bond isk (i.e., they ve eliminated $00 million woth o R.E. isk exposue, again because vitually all o the quately isk in R.E. investment is in the appeciation etun, and the ixed spead is iskless).
9 How Deivatives Wok: An Example... Littleton (long position) coves thei exposue to the ixed spead by holding $00 million o iskee bonds in thei potolio. Southen (shot position) coves thei exposue to the loating leg (NPI appeciation etun) by holding $00 million o eal estate (simila to NCREIF popeties) in thei potolio.
10 Deivatives o Potolio Balance How Littleton might have aived at thei $00 million long puchase: Littleton peviously had total potolio $300 million invested 50%/50% Stocks & Bonds. They want to move to equal shaes Stocks, Bonds & Real Estate (o divesiication): Fist Littleton sells $50 million in Stocks & invests poceeds in bonds, so: Now Littleton has $00 million in Stocks (= taget) and $200 million in bonds (= taget $00 million). Bond investment ove taget is invested in iskee bonds ($00 million to cove ixed spead in R.E. deivative). Next Littleton buys $00 million long position in R.E. appeciation etun swap (equies zeo cash investment). Littleton now eectively has isk exposue like $00 million each in Stocks, Bonds, Real Estate, although actually still owns $200 million in bonds.
11 Deivatives o Potolio Balance Littleton could accomplish this same esult by buying $00 million woth o popeties o pivate R.E. investment unds. Howeve: Tansaction costs & management ees might be highe than deivative ees. Eectively ewe numbe o popeties (even in a und) would add noise and/o basis isk compaed to deivative that tacks NPI benchmak. Thee might be less liquidity o a longe hoizon ixed commitment (less investment lexibility), cetainly with diect popety investment, possibly with und investment (depending on type o und).
12 Anothe consideation: Deivative Risk vs Popety Risk om a Potolio Pespective Fo popety etuns to be as liquid as deivative etuns, popety etuns must be based on tansaction pices. Deivative etuns ae based on an appaisal-based index (at least in the case o NPI & IPD), which might have moe avoable isk chaacteistics (due to smoothing ). (This consideation is bette o the long position than the shot.)
13 How Southen might have aived at thei $00 million shot puchase: Pevious Southen Potolio: Stocks: $3333 M (55%) Bonds: $88 M (30%) R.E.: $ 909 M (5%) Total: $6060 M (00%) Ate 20% Stock Cash, Potolio: Stocks: $2667 M (49%): Δ - $666 M Bonds: $88 M (34%): Δ 0 R.E.: $ 909 M (7%): Δ 0 Total: $5394 M (00%): Δ - $666 M Southen is now below-taget in Stocks, above in bonds & R.E. (aka denominato eect ) Can coect (ebalance) by: Puchase (Sale): Stocks: $300 M (% o pevious) Bonds: ($200 M) (% o pevious) R.E.: ($00 M) (% o pevious) Total Net:$ 0 M (0% o pevious) Southen can accomplish this by... Deivatives o Potolio Balance New Potolio: Stocks: $ = 2967 M (55%) Bonds: $ = 68 M (30%) R.E.: $ = 809 M (5%) Total: $ = 5394 M (00%)
14 Puchase (Sale): Stocks: $300 M (% o pevious) Bonds: ($200 M) (% o pevious) R.E.: ($00 M) (% o pevious) Total Net:$ 0 M (0% o pevious) Southen can accomplish the above by: Shot $00 M R.E. Deivative (0 cash low); Deivatives o Potolio Balance New Potolio: Stocks: $ = 2967 M (55%) Bonds: $ = 68 M (30%) R.E.: $ = 809 M (5%) Total: $ = 5394 M (00%) Cove R.E. shot by eamaking $00 M woth o R.E. (like NCREIF) to cove loating leg (R.E. appeciation), theeby educing R.E. isk exposue to $809 M; Shot $00 iskless bonds (T-Bond utues mkt) ($00 M cash low), coveed by R.E. Deivative ixed spead, so no impact on potolio isk exposue; Sell $200 M bonds ($200 M cash low), educing bond exposue to $68 M; Use esulting $300 M cash low to puchase stocks, binging exposue to $2967 M. Without having to actually sell any popeties.
15 Deivatives o Potolio Balance Southen could take a moe taditional appoach o simply boowing an incemental $00 million against thei R.E. potolio. Howeve: Covenants o estictions may pevent such boowing; Boowing tansaction costs and ees may exceed those o deivative; Inteest ates may make boowing NPV < 0 tansaction o tax-exempt investo (maginal boowe in debt mkt is taxed); And anyway this will not actually poduce the taget isk & etun allocation
16 Deivatives o Potolio Balance The esult o simply boowing $00 million against thei R.E. potolio may educe the eal estate equity on Southen s books to $809 million, but it inceases the leveage o thei eal estate, theeby etaining the isk and etun impact o the ull $909 million eal estate asset holding in the potolio. The boowing is like shoting bonds, theeby negating anothe $00 million o bond investment in the potolio isk/etun poile, esulting in the ollowing eective potolio allocation: New Potolio: Stocks: Use poceeds to buy stock: $ = 2967 M (55%) Bonds: Sell $200 M woth: $ = 58 M (28%) R.E.: Boow $00 M like shoting bonds: $ = 909 M (7%) Total: $ = 5394 M (00%) The only way to poduce the taget esult without the use o the deivative is by actually selling $00 million woth o Southen s R.E. popeties.
17 Othe Deivative Poducts The Popety Secto Swap Swap total etun o one NPI sub-index o total etun o anothe plus/minus a ixed leg (that might equal zeo). Useul o potolio ebalancing. To bette match benchmak (educe a type o systematic basis isk ). To speculate (make a bet) on one secto whee you eel you have supeio knowledge.
18 Deivatives o Hedging & Speculation Pevious example showed use o deivative o potolio balancing o taget allocation puposes. Thee is anothe majo use o deivatives: Speculation & Hedging
19 Using Deivatives to Make Money in a Down Maket Suppose you think the eal estate maket (& NPI) is headed down. You stand to lose money, even though you ae a good eal estate asset manage. You can use the shot position in the NPI appeciation o total etun utue to continue to make money in the down maket
20 Using Deivatives to Make Money in a Down Maket Example: You think NPI appeciation will be negative %/qt ove next 2 yeas. You eel you have positive alpha (supe-nomal etun due to supeio asset mgt). O it could simply be you have lowe-isk (less cyclical) popeties. (This would be beta ). So you appeciation will be only negative 0.5%/qt ove the same peiod. How can you use the swap contact?...
21 Using Deivatives to Make Money in a Down Maket Say you shot $00 million o NPI appeciation utues. I you expectations ae bon out, you will eceive $ million pe qt om the deivative, plus the ixed spead (which howeve will pobably be negative, hence paid by you). You lose only about $500,000 pe qt on you popety evaluations, leaving you net positive by $500,000 beoe counting the ixed spead. I the ixed spead is geate than negative 50 basis-points, you will make money on popety appeciation in a down maket! (You o couse also still have you popeties cash yield.)
22 Even i you don t have positive alpha, shoting the appeciation deivative hedges the down side o the eal estate maket. Even i you don t ully cove you popety position, you can educe downside volatility by shoting the appeciation swap. This is like: Using Deivatives to Make Money in a Down Maket Popety Maket Insuance I you have it when the maket is headed down, you will likely beat the benchmak, and you will beat the peomance o othe potolio manages who haven t hedged.
23 Picing the appeciation swap Thee ae two majo appoaches to analyzing the picing (o valuation) o the eal estate index swap: Abitage Analysis Equilibium Analysis The two appoaches give identical esults when the undelying index is always valued at the equilibium (liquid maket) value o its constituent popeties. Thee is also a useul methodology o valuing any swap contact: Cetainty Equivalence DCF Analysis (CEQ) CEQ valuation is based on equilibium analysis, but gives esults identical to both abitage and equilibium analysis when the undelying index is at equilibium value.
24 Abitage Analysis... Fist conside an abitage analysis... Suppose it wee possible to hold and eiciently tade long and shot positions in the NPI diectly (a so-called spot maket o the NPI), such that: Possible to constuct a iskless hedge between the undelying asset and the swap contact: Then we could deive a picing elationship like the classical Futues-Spot Paity Theoem... (Aside note: This implies that the index must itsel diectly elect equilibium pice and etun expectations.) We ll come back to this point late
25 Abitage Analysis... Let: V t = Value level o the undelying appeciation index at end o peiod t. E[y] = Expected income etun o the undelying index (assumed constant & iskless).* = Riskee inteest ate (e.g., LIBOR). F = Fixed leg (spead) paid om long to shot position (in pecent o notional value). The pice o the swap contact is given by F, the value o the ageed-upon ixed spead. F can be deived by abitage analysis as ollows...
26 Conside a 2-peiod appeciation swap. Constuct a iskless hedge as ollows: Cash Flow Today(t) Cash Flow End o Qt(t) Cash Flow End o Qt(t2) Shot position in Index V t -g t V t - E[y]V t -g t2 V t - E[y]V t - V t Invest isklessly zeocoupon Long position in appeciation swap -V t / ( ) 2 0 V t 0 g t V t - FV t g t2 V t - FV t Hedge Potolio = Sum (-/( ) 2 )V t -(FE[y])V t -(FE[y])V t iskless iskless
27 O on the othe side, the iskless hedge o the shot Cash Flow Today(t) Cash Flow End o Qt(t) Cash Flow End o Qt(t2) Long position in NPI -V t g t V t E[y]V t g t2 V t E[y]V t V t Boow isklessly zeocoupon Shot position in appeciation swap V t / ( ) 2 0 -V t 0 -g t V t FV t -g t2 V t FV t Hedge Potolio = Sum -(-/( ) 2 )V t (FE[y])V t (FE[y])V t iskless iskless
28 Suppose you pay a cash pice C t at time t o the long position in the swap. You can constuct the hedge descibed peviously by shoting the index and investing in a iskless zeo-coupon bond o a net cash low at time t o: (- /( ) 2 )V t, and theeby convet you utue cash low steam into a iskless one o -(F E[y])V 0 each utue peiod. Thus, including the C t cost o the swap, the NPV o you tansaction at time t is: Conside a 2-peiod appeciation swap. Constuct a iskless hedge as ollows: ( ) ( ) ( ) ( ) ] [ ] [ ) ( t V y E F V y E F C V long NPV = Since in act the swap is puchased o zeo net cash up-ont at time t, C t = 0, and the NPV o the long position in the appeciation swap is: ( ) ( ) ( ) ( ) ] [ ] [ ) ( V y E F V y E F V long NPV =
29 To avoid abitage, this NPV must equal zeo, so the abitageavoidance pice F o the appeciation swap is ound by setting the pevious equation equal to zeo and solving o F : Conside a 2-peiod appeciation swap. Constuct a iskless hedge as ollows: ( ) ( ) ( ) ( ) ( ) ( ) ] [ ] [ ] [ ] [ ] [ y E F y E F V y E F V y E F V y E F V = = = =
30 In geneal, the pice F is given by the ollowing equation: Extension to a T-peiod swap... F = E[y] ( ) ( ) ( ) ( ) ( ) ( ). ], [ ] [ ] [ ] [ ] [ any T y E F y E F V y E F V y E F V y E F V T T T = = = = L
31 Abitage Analysis... The ixed spead (F ), pice o the appeciation swap, equals the iskee inteest ate minus the eal estate income etun. Let: E[RP V ] = E[ V ] = Real Estate (index) Risk Pemium E[g] = Real Estate Expected Appeciation Rate E[y] = E[ V ] E[g] = Real Estate Income Retun (constant) Shot position ist buys the notional amount o eal estate and eceives expected total etun o: E[ V ] = E[RP V ] = E[g] E[y] But then swaps g t o F (eplaces g t with F) duing the contact, theeby eliminating all isk duing that time, hence eliminates any need o E[RP V ], giving a equied expected etun o: FE[y] =, which implies: F = - E[y] Note that this is independent o E *
32 Abitage Analysis... The ixed spead (F ), pice o the appeciation swap, equals the iskee inteest ate minus the eal estate income etun. Note that: F = E[y] F = (E[ V ] E[g] ) = E[g] (E[ V ] ) F = E[g] E[RP V ] The ixed spead (F ), pice o the appeciation swap, equals the expected index appeciation ate ( E[g] ) minus the index expected etun isk pemium ( E[RP V ] ). I E[RP V ] is constant, this implies that the utues pice ( F ) moves one-o-one with the expected index appeciation, E[g].
33 Abitage Analysis... F = E[y] F = E[g] E[RP V ] I E[RP V ] is constant, this implies that the utues pice ( F ) moves one-o-one with the expected index appeciation, E[g]. Howeve, it is impotant to note that: As long as the undelying index is piced at its equilibium value (which it would have to be i we could eally use it to constuct abitages), F will not necessaily o pimaily elect E[g], but athe: The equilibium swap pice will pimaily elect inteest ates and eal estate income etuns, accoding to: F = E[y]. In othe wods: I the index is piced at equilibium, changes ove time in E[g] may lagely elect coesponding changes in the maket s equilibium E[RP V ] equiement o eal estate, except as elected in changes in E[y].
34 Abitage Analysis... The complete abitage valuation omula o the t-peiod appeciation swap: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ] [, ] [ ] [ ] [ ) ( V y E F T o V y E F V y E F V y E F V long NPV T T T = = = = L The NPV o the shot position is just the negative o the above. Note: F should include impact o ees. E[y] can be equivalently expessed as: E[ V ] E[g] (Caution: This assumes V 0 is an equilibium value: no index lag.)
35 Fo total etun swap, the iskless hedge o the shot Cash Flow Today(t) Cash Flow End o Qt(t) Cash Flow End o Qt(t2) Long position in NPI -V t t V t t2 V t V t Boow isklessly zeocoupon Shot position in total etun swap V t / ( ) 2 0 -V t 0 - t V t FV t - t2 V t FV t Hedge Potolio = Sum -(-/( ) 2 )V t FV t FV t iskless iskless
36 Conside a 2-peiod total etun swap. Constuct a iskless hedge as ollows: Suppose you pay a cash pice C t at time t o the shot position in the swap. You can constuct the hedge descibed peviously by buying the index and isklessly boowing V t /( ) 2 zeo-coupon o 2 peiods, o a net cash low at time t o: -(-/( ) 2 )V t, and theeby convet you utue cash low steam into a iskless one o FV t each utue peiod. Thus, including the C t cost o the swap, the NPV o you tansaction at time t is: NPV ( shot) = 2 0 t ( ) ( ) 2 V C Since in act the swap is puchased o zeo net cash up-ont at time t, C t = 0, and the NPV o the shot position in the total etun swap is: NPV ( shot) = FV t FV ( ) 2 t ( ) 2 V FV t FV t t
37 To avoid abitage, this NPV must equal zeo, so the abitageavoidance pice F o the total etun swap is ound by setting the pevious equation equal to zeo and solving o F : Conside a 2-peiod total etun swap. Constuct a iskless hedge as ollows: ( ) ( ) ( ) t t t t F FV FV FV V = = = 2 2 2
38 Equilibium Analysis... In eal estate we cannot constuct the abitage, because we cannot diectly tade the undelying index. Howeve, the abitage analysis gives a picing esult that equates the expected total etun isk pemium pe unit o isk within and acoss the elevant asset makets: so-called linea picing E[] E[RP] Risk This is a chaacteistic o equilibium picing, which may also be viewed as nomative (i.e., ai ) picing.
39 Littleton s expected oveall net etun is: Fom the Pespective o the Coveed Long Position NPI Appeciation Retun (E L [g NPI ]), minus the Fixed Spead (F ), plus the iskee ate ( ) that they eceive on thei coveing bond investment. Littleton s oveall net isk exposue is that o the NPI: Because almost all etun isk is in the appeciation etun component. Theeoe, Littleton equies: E L [g NPI ] F E[RP NPI ]
40 Southen s expected oveall net etun is: Fom the Pespective o the Coveed Shot Position Thei expected Total Retun on thei ( eamaked ) coveing eal estate potolio (E S [ S ]) (which is simila to the NPI in isk), plus the Fixed Spead (F ), minus the expected NPI Appeciation Retun (E S [g NPI ] ). Southen s oveall net isk exposue is nil: Because thei exposue to the NPI appeciation obligation is coveed, and eal estate cash yield ( E[y] ) is nealy constant. Theeoe, Southen equies: F E S [g NPI ] E S [ S ]
41 Equilibium Analysis... Putting the two pevious picing conditions om each side togethe, we have the ollowing easible picing ange o F : E S [ S ] E S [g NPI ] F E L [g NPI ] E[RP NPI ] I all paties have the same expectations, the above picing condition becomes: E[ NPI ] E[g NPI ] F E[g NPI ] E[RP NPI ] ( E[RP NPI ]) E[g NPI ] F E[g NPI ] E[RP NPI ] E[RP NPI ] E[g NPI ] F E[g NPI ] E[RP NPI ] F = E[g NPI ] E[RP NPI ] = E[y NPI ] which is the same as the abitage-based esult*.
42 Equilibium Analysis... F = E[g NPI ] E[RP NPI ] = E[y NPI ] In this deivation we have not assumed that the undelying index is piced at its equilibium value. Howeve, i the undelying index is piced at its equilibium value, then the same obsevations as beoe apply to the equilibium pice and valuation o the swap contact. In paticula: Swap pice and value ae: Independent o Index Expected Retun E[ V ]. Independent o Index Expected Appeciation E[g]. Except in both cases as these expectations ae elected in E[y]. (i.e., movements in equilibium E[g] & E[RP V ] may lagely cancel.) Independent o the Volatility o the undelying Index.
43 Equilibium Analysis... F = E[g NPI ] E[RP NPI ] = E[y NPI ] Thee is an impotant coollay to this obsevation: I eal estate swap pices (speads) ae obseved to move noticeably with: Then: Changes in Index Expected Retuns going owad E[ V ], OR Changes in Index Expected Appeciation going owad E[g], Beyond the movements implied by changes in E[y], The undelying index is not piced at equilibium (e.g., the index value may be lagged behind cuent popety maket equilibium values due to the eect o appaisal valuation and/o othe index constuction issues.)
44 Appeciation vs Total Retun Swaps o Fixed Speads F = E[g NPI ] E[RP NPI ] = E[y NPI ] Fo the appeciation swap this picing ule will oten give a negative value o F (that is, shot paty pays the ixed spead to the long paty). This will almost always be tue i the undelying index is piced at its equilibium value. This is because the appeciation etun is only action o the total etun that is equied to compensate investos o beaing eal estate investment isk, And the swap long position that beas that isk only eceives the appeciation etun, not the total etun. I the swap contact is witten on the total etun (E[ NPI ]) instead o just the appeciation, we obtain by the same easoning as above (just substitute E[ NPI ] o E[g NPI ] in the above): F = E[ NPI ] E[RP NPI ] = ( is o couse nomally positive.*)
45 Typical Numbes F = E[g NPI ] E[RP NPI ] = E[y NPI ] The long-tem histoical aveage quately etun components o the NPI ae as ollows ( ): E[g NPI ] = 0.46% E[RP NPI ] = 0.90% =.5% E[y NPI ] =.94% Which implies a long-tem aveage appeciation pice, F o: F = 0.46% 0.90% =.5%.94% = 0.43%
46 Equilibium Analysis... Anothe coollay: I the appeciation swap is piced with a positive spead (F > 0), It is a stong signal that the undelying index is undepiced elative to the actual cuent maket value o the eal estate it epesents: Index value below its equilibium level implies expected nea-tem utue etuns to the index above thei equilibium ates. This could be due to index lag ate a ecent upsuge in popety maket value. (e.g., 2006.)
47 Suppose ove the peiod o the contact: Eect o Heteogeneous Expectations The potential long paty expects g NPI will ovepeom 25 bps/qt above the geneal maket expectation: E L [g NPI ] = E[g NPI ] 25bps. The potential shot paty is elatively beaish: E S [g NPI ] = E[g NPI ] 25bps. Suppose uthe that the potential shot paty eels that thei own (coveing) eal estate potolio will beat the NPI total etun by an aveage o 25bps/qt (even though it contains the same isk as the NPI, i.e., the excess is alpha ): E S [ S ] = E S [ NPI ] 25bps
48 Eect o Heteogeneous Expectations Plugging these expectations into ou picing omula o the appeciation swap, we obtain: E S [ S ] E S [g NPI ] F E L [g NPI ] E[RP NPI ] E S [RP S ] E S [g NPI ] F E L [g NPI ] E[RP NPI ] (E[RP NPI ] 25bps) (E[g NPI ] 25bps) F (E L [g NPI ] 25bps) E[RP NPI ] E[RP NPI ] E[g NPI ] 50bps F E[g NPI ] E[RP NPI ] 25bps Such complementay heteogeneous expectations add 75 bps to the easible pice ange o F. (e.g., instead o F = -0.43bp, we could have: -0.93% F -0.8%, with the exact pice ageed in negotiation.) Similaly, incompatible heteogeneous expectations (beaish long, bullish shot ) will eliminate any possible satisactoy F value, making tading ineasible.
49 Type o Heteogeneity Useul o Tading Implication o the act that the zeo-npv pice condition can be expessed in eithe o two ways: E[g] E[RP] OR E[y] Apat om alpha consideations, in ode to obtain complementay (ovelapping) pice equiements, we equie: Heteogeneity in g NPI expectations that ae not canceled out by heteogeneity in RP NPI expectations. This equies: Osetting E[g NPI ] & E[y NPI ] expectations. e.g.: I the long paty believes that NPI appeciation will be %/yea highe than aveage it must also believe that NPI income yields will be %/yea lowe than aveage.
50 Eect o Tansaction Fees Tansaction ees naow the easible tading ange. I the ees ae basis-points o notional value pe peiod (chaged to each paty), then the easible picing ange becomes: E S [ S ] E S [g NPI ] F E L [g NPI ] E[RP NPI ] Fees chaged to both paties togethe must be less than: E L [g NPI ] E S [g NPI ] E S [ S ] E[RP NPI ] This would seem to equie complementay heteogeneous expectations in ode to allow any easible tading ange. Howeve,...
51 Eect o Tansaction Fees The above analysis ignoes the savings o tansactions costs, investment management ees, and othe advantages o using deivatives vesus taditional methods o accomplishing the potolio balancing o hedging/speculation objectives undelying the shot and long positions. Fo example, suppose the long paty would avoid 20 bp/qt in investment management and und ees, and suppose the shot paty eectively saves 0 bp/qt in costs o boowing against thei potolio (altenative taditional methods to accomplish potolio balancing objectives). Then even with homogeneous expectations, thee exists 30 bp/qt o savings that can be split among the two paties and the bokes and investment banking ees o the deivative pocess.
52 What about pedictability in the NPI? Appaisal smoothing and stale appaisals (along with tue undelying popety maket sluggishness) give the NPI much moe inetia than typical secuities indexes, making the NPI elatively smooth and pedictable. Wouldn t this type o pedictability esult in an absence o heteogeneous expectations, and theeby an absence o countepaties o tading the deivatives, making a unctioning utues maket impossible?
53 What about pedictability in the NPI? Answe: Not necessaily. As seen in ou Littleton & Southen example, deivative tades may have easons othe than speculation o tading deivatives. Heteogeneous expectations may not be necessay. Pedictability in the NPI will simply come out in the equilibium deivative pice, F. Recall that F is a unction o the maket paticipants expectations about the utue NPI appeciation etuns: E L [g NPI ] and E S [g NPI ]. e.g., i NPI is headed down, then E[g NPI ] will be negative, making F moe negative than it would othewise be (meaning the shot position must pay the long position moe in the ixed leg). Well-unctioning utues makets have long existed o vaious commodities and inancial poducts whose utue pice diections ae oten athe pedictable in advance (e.g., con, wheat, oil, oeign exchange, among othes).
54 What about pedictability in the NPI? O couse, pedictability in the NPI means that deivatives tades who don t want to get taken advantage o must use all the elevant inomation as skillully as possible to be educated about what ae easonable expectations o whee the NPI is headed. Fo example (inte alia ), the MIT tansactions-based index (which tends to lead the NPI ) Roughly speaking: g NPI (y t) = (/2)g TBI (y t-) (/2)g TBI (y t).
55 What about pedictability in the NPI? Eect o Index Lag on Swap Picing and Valuation: Index Lag Index will oten not be valued at its equilibium value. That is, ealistic expected etuns on the index die in the nea-tem om long-un equilibium ates. In such cicumstances, the Abitage Picing and Valuation Fomula o the swap no longe holds. The zeo-npv picing condition will still be well appoximated by: F = E[g] E[RP V ] but not by E[y], and only povided that E[RP V ] in the above omula elects the maket s long-un equilibium isk pemium, not the cuent disequilibium pemium pesented by the index (while E[g] elects the non-equilibium appeciation in the index).
56 Altenative Picing Pespectives The pevious picing analysis assumed tading by coveed paties on both sides. Altenative picing pespectives ae possible Suppose neithe paty is coveed at all, and both view themselves as equiing a etun as i they wee actually making the notional investment. The esulting picing condition would be: E S [g NPI ] E[RP NPI ] F E L [g NPI ] E[RP NPI ] Which implies a easible picing ange o F o width: E[g L NPI ] E[gS NPI ] 2 This equies that the long position be substantially moe bullish than the shot position. But this pespective is not based on an equilibium amewok...
57 Altenative Picing Pespectives We can analyze equilibium picing o the uncoveed swap by using cetaintyequivalence valuation (CEQ) Conside a -peiod binomial wold; V 0 = Cuent value o the R.E.index & notional amt o swap tade; p = Pobability o the up move in index next peiod (eal pob) V up, V down = Value o index next peiod in up o down outcomes; g = -peiod appeciation etun on index; F = Appeciation swap pice (ixed leg) in action o notional tade amount. V 0 p -p V up V down V up V down = ( g up )V 0 = ( g down )V 0 E[V ] = ( E[g])VE 0 = [p(g[ up ) (-p)(g = [ pg up (-p)g down E[g] ] = pg up (-p)g down (g down )]V 0 down ]V 0
58 Altenative Picing Pespectives Cash low amts o appec swap long position: CF up = (g up F)V 0 Expected CF next peiod is: E[CF ] = [pg[ up (-p)g down = ( E[g] F )V 0 down ]V 0 FV 0 Cetainty Equivalent CF next peiod is: 0 p -p CF down = (g down F)V 0 CEQ[CF CF ] = E[CF ] E[RP V ](CF CF up up CF CF down )/( )/(V up /V 0 V down /V 0 ) = E[CF ] ( E[ V ] )(g up g down )V 0 / (g( up g down ) = E[CF ] ( E[ V ] )V 0 down /V Hence, pesent value o uncoveed swap CF next peiod is: PV[CF ] = [ E[CF ] ( E[ V ] )V 0 ] / ( ) In equilibium, this must equal the 0 net CF o the tade today: PV[CF ] = [ E[CF ] ( E[ V ] )V 0 ] / ( ) = 0. E[CF ] = ( E[ V ] )V 0
59 Altenative Picing Pespectives Thus, we have the equilibium condition: p CF up = (g up F)V 0 E[CF ] = ( E[] )V 0 ( E[g] F )V 0 = ( E[] )V 0 F = E[g] E[] ] = E[g] E[RP] 0 -p CF down = (g down F)V 0 = E[y] This is the same equilibium picing condition that we obtained beoe: F = E[g] E[RP] = E[y]
60 PV[ C T CEQ0[ C ] ] = T T ( ) = Cetainty Equivalence Valuation E [ C 0 T STD C 0[ ] ] ± STD 0[ V ] o Deivatives In geneal, we can use cetainty-equivalence discounting to evaluate the swap with heteogeneous expectations, and whethe o not the undelying index is valued at its equilibium level The geneal cetainty equivalence valuation (CEQ) omula o valuing a deivative cash low is as ollows: Let: C t = The deivative value (cash low) t peiods hence, E[ V ] = Equilibium expected total etun on undelying asset (pe peiod). Then the Cetainty Equivalence PV omula is as ollows o a single sum T peiods in the utue, with isk accumulation thoughout T ):* T T ( E[ ]) ( ) ) ( ) T V The isk adjustment is subtacted o long positions, added o shots.
61 Cetainty Equivalence Valuation o Deivatives Fo the index swap, the CEQ valuation omula o a given utue cash low o the swap t peiods in the utue (C t ) with cuent value o the undelying index (= notional amount o tade) V 0 is: PV [ C 0 t ] = CEQ0[ Ct ] = = t ( ) 0 E [ C t ] ± E0[ Ct ] ± = E [ C 0 ( E[ RP ]) t ( ) ( E[ RP ]) t ( ) V V t ] ± ( E[ RP ]). t ( ) STD[ V ] V STD[ V ] V 0 V STD[ C STD[ V whee E[RP V ] is the mkt equilibium isk pemium. 0 t ] ] Whee the isk adjustment in the numeato is subtacted o long positions and added o shot positions (negative coel betw swap & index). Thee is only peiod o isk accumulation (just pio to the cash low), because the cash low is based solely on the index etun in peiod t times a notional amount that is ixed up ont at time 0. Hence, the isk adjustment in the numeato is o just one peiod.
62 Conside a -peiod example with F = -60bp and the ollowing expectations: Long Pespective: = 0.75% /qt Shot Pespective: E L [ NPI ] = 2.00% /qt E S [ NPI ] = 2.00% /qt E L [g NPI ] = 0.75% /qt Cetainty Equivalence Valuation o Deivatives E S [g NPI ] = 0.55% /qt E L [RP NPI ] =.25% /qt E S [RP NPI ] =.25% /qt E L [C ] = ( ( ))$00 E S [C ] = ( ( ))$00 = $0.75 $0.60 = $.35. = -$0.55 $0.60 = -$.5. Applying the cetainty equivalence DCF valuation omula: PV PV S L ( E[ RP ]) V $.35 (.025) L E [ Ct ] V $00 $.35 $.25 [ Ct ] = = = R = ( E[ RP ]) V $.5 (.025) S E [ Ct ] V $00 $.5 $.25 [ Ct ] = = = R = $ $ Because o heteogeneous expectations, The tade allows both sides to ace a positive NPV ex ante.
63 PV PV S L Cetainty Equivalence Valuation o Deivatives ( E[ RP ]) V $.35 (.025) L E [ Ct ] V $00 $.35 $.25 [ Ct ] = = = R = ( E[ RP ]) V $.5 (.025) S E [ Ct ] V $00 $.5 $.25 [ Ct ] = = = R = $ $ PV[C] = CEQ[C] / ( ) = $0.0 /.0075 = $ Even though the expected cash low is $.35 o the long position, - $.5 o the shot position, the cetainty equivalent cash low is only $0.0 in both cases. The cetainty-equivalence opeation eveses the sign o the shot position cash low expectation, because the isk in the shot position is negative the isk in the undelying index, because the two ae peectly negatively coelated. Note that you should always employ the maket equilibium isk pemium o the undelying index.
64 NPV L = $ Same thing using the abitage ( F Ey) ( ) NPV long = NPI T ( ) = $00 (.0075).0075 = *0.3333*$00 = $ omula Given the same conditions as beoe with F = -0.60%: = 0.75% /qt E L [ NPI ] = 2.00% /qt E S [ NPI ] = 2.00% /qt E L [g NPI ] = 0.75% /qt E S [g NPI ] = 0.55% /qt Deine: Ey L = E L [ NPI ] E L [g NPI ] = 2%.75% =.25% Ey S = E S [ NPI ] E S [g NPI ] = 2%.55% =.45% Applying the abitage valuation omula to the $00 notional tade: ( F Ey) NPV ( long) = NPI T ( ) = $00 (.0075).0075 = *0.3333*$00 = $ NPV S = $ Same answe as beoe. (But this omula only woks i the undelying index is in equilibium.) See downloadable Excel ile example on book CD 0
Chapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
More informationHow Much Should a Firm Borrow. Effect of tax shields. Capital Structure Theory. Capital Structure & Corporate Taxes
How Much Should a Fim Boow Chapte 19 Capital Stuctue & Copoate Taxes Financial Risk - Risk to shaeholdes esulting fom the use of debt. Financial Leveage - Incease in the vaiability of shaeholde etuns that
More informationGESTÃO FINANCEIRA II PROBLEM SET 1 - SOLUTIONS
GESTÃO FINANCEIRA II PROBLEM SET 1 - SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE 1 ST SEMESTER 2010-2011 Chapte 1 The Copoation 1-13. What is the diffeence
More informationContinuous Compounding and Annualization
Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem
More informationCONCEPT OF TIME AND VALUE OFMONEY. Simple and Compound interest
CONCEPT OF TIME AND VALUE OFMONEY Simple and Compound inteest What is the futue value of shs 10,000 invested today to ean an inteest of 12% pe annum inteest payable fo 10 yeas and is compounded; a. Annually
More informationest using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.
9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,
More informationExam #1 Review Answers
xam #1 Review Answes 1. Given the following pobability distibution, calculate the expected etun, vaiance and standad deviation fo Secuity J. State Pob (R) 1 0.2 10% 2 0.6 15 3 0.2 20 xpected etun = 0.2*10%
More informationDefinitions and terminology
I love the Case & Fai textbook but it is out of date with how monetay policy woks today. Please use this handout to supplement the chapte on monetay policy. The textbook assumes that the Fedeal Reseve
More informationValuation of Floating Rate Bonds 1
Valuation of Floating Rate onds 1 Joge uz Lopez us 316: Deivative Secuities his note explains how to value plain vanilla floating ate bonds. he pupose of this note is to link the concepts that you leaned
More information9:6.4 Sample Questions/Requests for Managing Underwriter Candidates
9:6.4 INITIAL PUBLIC OFFERINGS 9:6.4 Sample Questions/Requests fo Managing Undewite Candidates Recent IPO Expeience Please povide a list of all completed o withdawn IPOs in which you fim has paticipated
More informationAMB111F Financial Maths Notes
AMB111F Financial Maths Notes Compound Inteest and Depeciation Compound Inteest: Inteest computed on the cuent amount that inceases at egula intevals. Simple inteest: Inteest computed on the oiginal fixed
More informationINITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS
INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in
More informationFI3300 Corporate Finance
Leaning Objectives FI00 Copoate Finance Sping Semeste 2010 D. Isabel Tkatch Assistant Pofesso of Finance Calculate the PV and FV in multi-peiod multi-cf time-value-of-money poblems: Geneal case Pepetuity
More informationThe Predictive Power of Dividend Yields for Stock Returns: Risk Pricing or Mispricing?
The Pedictive Powe of Dividend Yields fo Stock Retuns: Risk Picing o Mispicing? Glenn Boyle Depatment of Economics and Finance Univesity of Cantebuy Yanhui Li Depatment of Economics and Finance Univesity
More informationEquity compensation plans New Income Statement impact on guidance Earnings Per Share Questions and answers
Investos/Analysts Confeence: Accounting Wokshop Agenda Equity compensation plans New Income Statement impact on guidance Eanings Pe Shae Questions and answes IAC03 / a / 1 1 Equity compensation plans The
More informationThe LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.
Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the
More informationIlona V. Tregub, ScD., Professor
Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation
More informationDefine What Type of Trader Are you?
Define What Type of Tade Ae you? Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 1 Disclaime and Risk Wanings Tading any financial maket involves isk. The content of this
More informationFirstmark Credit Union Commercial Loan Department
Fistmak Cedit Union Commecial Loan Depatment Thank you fo consideing Fistmak Cedit Union as a tusted souce to meet the needs of you business. Fistmak Cedit Union offes a wide aay of business loans and
More informationAn Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei isk-ewad chaacteistics? The Finance Development Cente 2002 1 Fom
More informationHow To Find The Optimal Stategy For Buying Life Insuance
Life Insuance Puchasing to Reach a Bequest Ehan Bayakta Depatment of Mathematics, Univesity of Michigan Ann Abo, Michigan, USA, 48109 S. David Pomislow Depatment of Mathematics, Yok Univesity Toonto, Ontaio,
More informationVeröffentlicht auf. www.finexpert.info. Februar 2009
F 721 Veöentlicht au www.inexpet.ino Febua 29 COST OF CPITL ND VLUTION WITH IPERFECT DIVERSIFICTION ND UNSYSTETIC RISKS Ein Sevice von: FutueValue Goup G eail: Kontakt@FutueValue.de Intenet: www.futuevalue.de
More informationThings to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.
Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to
More informationControlling the Money Supply: Bond Purchases in the Open Market
Money Supply By the Bank of Canada and Inteest Rate Detemination Open Opeations and Monetay Tansmission Mechanism The Cental Bank conducts monetay policy Bank of Canada is Canada's cental bank supevises
More informationFinancial Planning and Risk-return profiles
Financial Planning and Risk-etun pofiles Stefan Gaf, Alexande Kling und Jochen Russ Pepint Seies: 2010-16 Fakultät fü Mathematik und Witschaftswissenschaften UNIERSITÄT ULM Financial Planning and Risk-etun
More informationSTUDENT RESPONSE TO ANNUITY FORMULA DERIVATION
Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts
More informationQuestions for Review. By buying bonds This period you save s, next period you get s(1+r)
MACROECONOMICS 2006 Week 5 Semina Questions Questions fo Review 1. How do consumes save in the two-peiod model? By buying bonds This peiod you save s, next peiod you get s() 2. What is the slope of a consume
More informationQuestions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing
M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow
More informationFinancing Terms in the EOQ Model
Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad
More informationSupply chain information sharing in a macro prediction market
Decision Suppot Systems 42 (2006) 944 958 www.elsevie.com/locate/dss Supply chain infomation shaing in a maco pediction maket Zhiling Guo a,, Fang Fang b, Andew B. Whinston c a Depatment of Infomation
More informationLoyalty Rewards and Gift Card Programs: Basic Actuarial Estimation Techniques
Loyalty Rewads and Gift Cad Pogams: Basic Actuaial Estimation Techniques Tim A. Gault, ACAS, MAAA, Len Llaguno, FCAS, MAAA and Matin Ménad, FCAS, MAAA Abstact In this pape we establish an actuaial famewok
More informationPersonal Saving Rate (S Households /Y) SAVING AND INVESTMENT. Federal Surplus or Deficit (-) Total Private Saving Rate (S Private /Y) 12/18/2009
1 Pesonal Saving Rate (S Households /Y) 2 SAVING AND INVESTMENT 16.0 14.0 12.0 10.0 80 8.0 6.0 4.0 2.0 0.0-2.0-4.0 1959 1961 1967 1969 1975 1977 1983 1985 1991 1993 1999 2001 2007 2009 Pivate Saving Rate
More informationarxiv:1110.2612v1 [q-fin.st] 12 Oct 2011
Maket inefficiency identified by both single and multiple cuency tends T.Toká 1, and D. Hováth 1, 1 Sos Reseach a.s., Stojáenská 3, 040 01 Košice, Slovak Republic Abstact axiv:1110.2612v1 [q-fin.st] 12
More informationTrading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract
Tading Volume and Seial Coelation in Stock Retuns in Pakistan Khalid Mustafa Assistant Pofesso Depatment of Economics, Univesity of Kaachi e-mail: khalidku@yahoo.com and Mohammed Nishat Pofesso and Chaiman,
More informationSaving and Investing for Early Retirement: A Theoretical Analysis
Saving and Investing fo Ealy Retiement: A Theoetical Analysis Emmanuel Fahi MIT Stavos Panageas Whaton Fist Vesion: Mach, 23 This Vesion: Januay, 25 E. Fahi: MIT Depatment of Economics, 5 Memoial Dive,
More informationBasic Financial Mathematics
Financial Engineeing and Computations Basic Financial Mathematics Dai, Tian-Shy Outline Time Value of Money Annuities Amotization Yields Bonds Time Value of Money PV + n = FV (1 + FV: futue value = PV
More informationYIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE
YIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE Septembe 1999 Quoted Rate Teasuy Bills [Called Banke's Discount Rate] d = [ P 1 - P 1 P 0 ] * 360 [ N ] d = Bankes discount yield P 1 = face
More informationTjalling C. Koopmans Research Institute
Tjalling C. Koopmans Reseach Institute Tjalling C. Koopmans Reseach Institute Utecht School of Economics Utecht Univesity Kiekenpitplein 1-3584 EC Utecht The Nethelands telephone +31 30 53 9800 fax +31
More informationSolutions to Problems: Chapter 7
Solution to Poblem: Chapte 7 P7-1. P7-2. P7-3. P7-4. Authoized and available hae LG 2; Baic a. Maximum hae available fo ale Authoized hae 2,000,000 Le: Shae outtanding 1,400,000 Available hae 600,000 b.
More informationIgnorance is not bliss when it comes to knowing credit score
NET GAIN Scoing points fo you financial futue AS SEEN IN USA TODAY SEPTEMBER 28, 2004 Ignoance is not bliss when it comes to knowing cedit scoe By Sanda Block USA TODAY Fom Alabama comes eassuing news
More informationA Capacitated Commodity Trading Model with Market Power
A Capacitated Commodity Tading Model with Maket Powe Victo Matínez-de-Albéniz Josep Maia Vendell Simón IESE Business School, Univesity of Navaa, Av. Peason 1, 08034 Bacelona, Spain VAlbeniz@iese.edu JMVendell@iese.edu
More informationCHAPTER 10 Aggregate Demand I
CHAPTR 10 Aggegate Demand I Questions fo Review 1. The Keynesian coss tells us that fiscal policy has a multiplied effect on income. The eason is that accoding to the consumption function, highe income
More informationUNIT CIRCLE TRIGONOMETRY
UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + = - - -
More informationIntertemporal Macroeconomics
Intetempoal Macoeconomics Genot Doppelhofe* May 2009 Fothcoming in J. McCombie and N. Allington (eds.), Cambidge Essays in Applied Economics, Cambidge UP This chapte eviews models of intetempoal choice
More informationData Center Demand Response: Avoiding the Coincident Peak via Workload Shifting and Local Generation
(213) 1 28 Data Cente Demand Response: Avoiding the Coincident Peak via Wokload Shifting and Local Geneation Zhenhua Liu 1, Adam Wieman 1, Yuan Chen 2, Benjamin Razon 1, Niangjun Chen 1 1 Califonia Institute
More informationChapter 7: Equilibrium in the Flexible Price Model
Copyight MHHE 2005 Chapte 7: Equilibium in the Flexible Pice Model knowing what has happened to consumption spending. But consumption spending depends on income, which in tun depends on the levels o net
More informationThe impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011
The impact of migation on the povision of UK public sevices (SRG.10.039.4) Final Repot Decembe 2011 The obustness The obustness of the analysis of the is analysis the esponsibility is the esponsibility
More informationProblem Set # 9 Solutions
Poblem Set # 9 Solutions Chapte 12 #2 a. The invention of the new high-speed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease
More informationEvaluating the impact of Blade Server and Virtualization Software Technologies on the RIT Datacenter
Evaluating the impact of and Vitualization Softwae Technologies on the RIT Datacente Chistophe M Butle Vitual Infastuctue Administato Rocheste Institute of Technology s Datacente Contact: chis.butle@it.edu
More information2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,
3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects
More informationThe transport performance evaluation system building of logistics enterprises
Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194-114 Online ISSN: 213-953 Pint ISSN: 213-8423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics
More informationAn Analysis of Manufacturer Benefits under Vendor Managed Systems
An Analysis of Manufactue Benefits unde Vendo Managed Systems Seçil Savaşaneil Depatment of Industial Engineeing, Middle East Technical Univesity, 06531, Ankaa, TURKEY secil@ie.metu.edu.t Nesim Ekip 1
More informationThe Incidence of Social Security Taxes in Economies with Partial. Compliance: Evidence from the SS Reform in Mexico
The Incidence of Social Secuity Taxes in Economies ith Patial Compliance: Evidence fom the SS Refom in Mexico Gecia M. Maufo Abstact Looking at impovements in social secuity benefits in Mexico, this pape
More informationSemipartial (Part) and Partial Correlation
Semipatial (Pat) and Patial Coelation his discussion boows heavily fom Applied Multiple egession/coelation Analysis fo the Behavioal Sciences, by Jacob and Paticia Cohen (975 edition; thee is also an updated
More information9.5 Amortization. Objectives
9.5 Aotization Objectives 1. Calculate the payent to pay off an aotized loan. 2. Constuct an aotization schedule. 3. Find the pesent value of an annuity. 4. Calculate the unpaid balance on a loan. Congatulations!
More informationConcept and Experiences on using a Wiki-based System for Software-related Seminar Papers
Concept and Expeiences on using a Wiki-based System fo Softwae-elated Semina Papes Dominik Fanke and Stefan Kowalewski RWTH Aachen Univesity, 52074 Aachen, Gemany, {fanke, kowalewski}@embedded.wth-aachen.de,
More informationImproving Network Security Via Cyber-Insurance A Market Analysis
1 Impoving Netwok Secuity Via Cybe-Insuance A Maket Analysis RANJAN PAL, LEANA GOLUBCHIK, KONSTANTINOS PSOUNIS Univesity of Southen Califonia PAN HUI Hong Kong Univesity of Science and Technology Recent
More informationON THE (Q, R) POLICY IN PRODUCTION-INVENTORY SYSTEMS
ON THE R POLICY IN PRODUCTION-INVENTORY SYSTEMS Saifallah Benjaafa and Joon-Seok Kim Depatment of Mechanical Engineeing Univesity of Minnesota Minneapolis MN 55455 Abstact We conside a poduction-inventoy
More informationPart VI: Active Portfolio Management
1 Potolio anagement Pime Pime I: Top-Down Potolio anagement Capital vs. sset allocation aowitz secuity selection model Pime II: sset Picing odels CP (Theoy & Pactice Index & ulti-facto odels Pime III:
More informationConverting knowledge Into Practice
Conveting knowledge Into Pactice Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 2 0 1 0 C o p y i g h t s V l a d i m i R i b a k o v 1 Disclaime and Risk Wanings Tading
More informationChapter 11: Aggregate Demand II, Applying the IS-LM Model Th LM t
Equilibium in the - model The cuve epesents equilibium in the goods maket. Chapte :, Applying the - Model Th t C ( T) I( ) G The cuve epesents money maket equilibium. M L(, ) The intesection detemines
More informationChannel selection in e-commerce age: A strategic analysis of co-op advertising models
Jounal of Industial Engineeing and Management JIEM, 013 6(1):89-103 Online ISSN: 013-0953 Pint ISSN: 013-843 http://dx.doi.og/10.396/jiem.664 Channel selection in e-commece age: A stategic analysis of
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance the availability
More informationNBER WORKING PAPER SERIES FISCAL ZONING AND SALES TAXES: DO HIGHER SALES TAXES LEAD TO MORE RETAILING AND LESS MANUFACTURING?
NBER WORKING PAPER SERIES FISCAL ZONING AND SALES TAXES: DO HIGHER SALES TAXES LEAD TO MORE RETAILING AND LESS MANUFACTURING? Daia Bunes David Neumak Michelle J. White Woking Pape 16932 http://www.nbe.og/papes/w16932
More informationThere is considerable variation in health care utilization and spending. Geographic Variation in Health Care: The Role of Private Markets
TOMAS J. PHILIPSON Univesity of Chicago SETH A. SEABUY AND Copoation LEE M. LOCKWOOD Univesity of Chicago DANA P. GOLDMAN Univesity of Southen Califonia DAIUS N. LAKDAWALLA Univesity of Southen Califonia
More informationSoftware Engineering and Development
I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining
More informationOver-encryption: Management of Access Control Evolution on Outsourced Data
Ove-encyption: Management of Access Contol Evolution on Outsouced Data Sabina De Capitani di Vimecati DTI - Univesità di Milano 26013 Cema - Italy decapita@dti.unimi.it Stefano Paaboschi DIIMM - Univesità
More informationPromised Lead-Time Contracts Under Asymmetric Information
OPERATIONS RESEARCH Vol. 56, No. 4, July August 28, pp. 898 915 issn 3-364X eissn 1526-5463 8 564 898 infoms doi 1.1287/ope.18.514 28 INFORMS Pomised Lead-Time Contacts Unde Asymmetic Infomation Holly
More informationLearning Objectives. Chapter 2 Pricing of Bonds. Future Value (FV)
Leaig Objectives Chapte 2 Picig of Bods time value of moey Calculate the pice of a bod estimate the expected cash flows detemie the yield to discout Bod pice chages evesely with the yield 2-1 2-2 Leaig
More informationSUGGESTED SOLUTIONS. 21404 Strategic Financial Management. CA Professional (Strategic Level II) Examination June 2014
SUGGESTED SOLUTIONS 21404 Stategic Financial Management CA Pofessional (Stategic Level II) Examination June 2014 THE INSTITUTE OF CHARTERED ACCOUNTANTS OF SRI LANKA All Rights Reseved Answe No. 01 (a)
More informationThe Personal-Tax Advantages of Equity
The Pesonal-Tax Advantages of Equity Richad C. Geen and Buton Hollifield Gaduate School of Industial Administation Canegie Mellon Univesity Decembe 23, 999 Discussions with Piee Collin Dufesne, Bob Dammon,
More informationModeling and Verifying a Price Model for Congestion Control in Computer Networks Using PROMELA/SPIN
Modeling and Veifying a Pice Model fo Congestion Contol in Compute Netwoks Using PROMELA/SPIN Clement Yuen and Wei Tjioe Depatment of Compute Science Univesity of Toonto 1 King s College Road, Toonto,
More informationMoney Market Funds Intermediation and Bank Instability
Fedeal Reseve Bank of New Yok Staff Repots Money Maket Funds Intemediation and Bank Instability Maco Cipiani Antoine Matin Buno M. Paigi Staff Repot No. 599 Febuay 013 Revised May 013 This pape pesents
More information4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero digit to
. Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate
More informationThe Binomial Distribution
The Binomial Distibution A. It would be vey tedious if, evey time we had a slightly diffeent poblem, we had to detemine the pobability distibutions fom scatch. Luckily, thee ae enough similaities between
More informationThe Supply of Loanable Funds: A Comment on the Misconception and Its Implications
JOURNL OF ECONOMICS ND FINNCE EDUCTION Volume 7 Numbe 2 Winte 2008 39 The Supply of Loanable Funds: Comment on the Misconception and Its Implications. Wahhab Khandke and mena Khandke* STRCT Recently Fields-Hat
More informationStrategic Asset Allocation and the Role of Alternative Investments
Stategic Asset Allocation and the Role of Altenative Investments DOUGLAS CUMMING *, LARS HELGE HAß, DENIS SCHWEIZER Abstact We intoduce a famewok fo stategic asset allocation with altenative investments.
More informationFinancial Derivatives for Computer Network Capacity Markets with Quality-of-Service Guarantees
Financial Deivatives fo Compute Netwok Capacity Makets with Quality-of-Sevice Guaantees Pette Pettesson pp@kth.se Febuay 2003 SICS Technical Repot T2003:03 Keywods Netwoking and Intenet Achitectue. Abstact
More informationLiquidity and Insurance for the Unemployed
Liquidity and Insuance fo the Unemployed Robet Shime Univesity of Chicago and NBER shime@uchicago.edu Iván Wening MIT, NBER and UTDT iwening@mit.edu Fist Daft: July 15, 2003 This Vesion: Septembe 22, 2005
More informationCONCEPTUAL FRAMEWORK FOR DEVELOPING AND VERIFICATION OF ATTRIBUTION MODELS. ARITHMETIC ATTRIBUTION MODELS
CONCEPUAL FAMEOK FO DEVELOPING AND VEIFICAION OF AIBUION MODELS. AIHMEIC AIBUION MODELS Yui K. Shestopaloff, is Diecto of eseach & Deelopment at SegmentSoft Inc. He is a Docto of Sciences and has a Ph.D.
More informationOpen Economies. Chapter 32. A Macroeconomic Theory of the Open Economy. Basic Assumptions of a Macroeconomic Model of an Open Economy
Chapte 32. A Macoeconomic Theoy of the Open Economy Open Economies An open economy is one that inteacts feely with othe economies aound the wold. slide 0 slide 1 Key Macoeconomic Vaiables in an Open Economy
More informationSpirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project
Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.
More informationExperimentation under Uninsurable Idiosyncratic Risk: An Application to Entrepreneurial Survival
Expeimentation unde Uninsuable Idiosyncatic Risk: An Application to Entepeneuial Suvival Jianjun Miao and Neng Wang May 28, 2007 Abstact We popose an analytically tactable continuous-time model of expeimentation
More informationA Note on Risky Bond Valuation
A Note on Risky Bond Valuation C. H. Hui Banking Poliy Depatment Hong Kong Monetay Authoity 0th Floo,, Gaden Road, Hong Kong Email: Cho-Hoi_Hui@hkma.gov.hk C. F. Lo Physis Depatment The Chinese Univesity
More informationContingent capital with repeated interconversion between debt and equity
Contingent capital with epeated inteconvesion between debt and equity Zhaojun Yang 1, Zhiming Zhao School of Finance and Statistics, Hunan Univesity, Changsha 410079, China Abstact We develop a new type
More informationMean-Reverting-Ebit-Based Stock Option Evaluation: Theory and Practice
Jounal of Applied Finance & aning, vol. 3, no. 5, 03, 35-36 ISSN: 79-6580 pint vesion, 79-6599 online Scienpess Ltd, 03 Mean-Reveting-bit-ased Stoc Option valuation: Theoy and Pactice Hassan l Ibami Abstact
More informationMERGER SIMULATION AS A SCREENING DEVICE: SIMULATING THE EFFECTS OF THE KRAFT/CADBURY TRANSACTION
MERGER SIMULATION AS A SCREENING DEVICE: SIMULATING THE EFFECTS OF THE KRAFT/CADBURY TRANSACTION Enique Andeu, Kisten Edwads, Aleando Requeo 1,2 Novembe 2010 Abstact In this aticle we pesent a method that
More informationFrom PLI s Treatise Initial Public Offerings: A Practical Guide to Going Public #19784 PREPACKAGED BANKRUPTCY AND PREARRANGED BANKRUPTCY PROCESS
Fom PLI s Teatise Initial Public Offeings: A Pactical Guide to Going Public #19784 16 PREPACKAGED BANKRUPTCY AND PREARRANGED BANKRUPTCY PROCESS Deyck Palme Jessica Fink Cadwalade, Wickesham & Taft LLP
More informationConfirmation of Booking
The Pesentes Rebecca Mogan Rebecca is a Taxation Consultant with the NTAA and has ove 15 yeas tax expeience. Rebecca holds a Bachelo of Ats and Law and a Mastes of Taxation. Rebecca has pesented a numbe
More informationInstructions to help you complete your enrollment form for HPHC's Medicare Supplemental Plan
Instuctions to help you complete you enollment fom fo HPHC's Medicae Supplemental Plan Thank you fo applying fo membeship to HPHC s Medicae Supplement plan. Pio to submitting you enollment fom fo pocessing,
More informationVector Calculus: Are you ready? Vectors in 2D and 3D Space: Review
Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.-7. find the vecto defined
More information1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2
Chapte 5 Example The helium atom has 2 electonic enegy levels: E 3p = 23.1 ev and E 2s = 20.6 ev whee the gound state is E = 0. If an electon makes a tansition fom 3p to 2s, what is the wavelength of the
More informationRisk Sensitive Portfolio Management With Cox-Ingersoll-Ross Interest Rates: the HJB Equation
Risk Sensitive Potfolio Management With Cox-Ingesoll-Ross Inteest Rates: the HJB Equation Tomasz R. Bielecki Depatment of Mathematics, The Notheasten Illinois Univesity 55 Noth St. Louis Avenue, Chicago,
More informationAN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM
AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,
More informationTransmittal 47 Date: FEBRUARY 24, 2006
anual ystem Pub 100-03 edicae National oveage Deteminations Depatment of Health & Human evices (DHH) ente fo edicae & edicaid evices () Tansmittal 47 Date: EBUAY 24, 2006 hange equest 4257 UBJET: hanges
More informationFixed Income Attribution: Introduction
18th & 19th Febuay 2015, Cental London Fixed Income Attibution: A compehensive undestanding of Fixed Income Attibution and the challenging data issues aound this topic Delegates attending this two-day
More informationLiquidity and Insurance for the Unemployed*
Fedeal Reseve Bank of Minneapolis Reseach Depatment Staff Repot 366 Decembe 2005 Liquidity and Insuance fo the Unemployed* Robet Shime Univesity of Chicago and National Bueau of Economic Reseach Iván Wening
More informationWELCOME TO OUR NEW NEWSLETTER
ISSUE ONE > JUNE 2013 WELCOME TO OUR NEW NEWSLETTER PARTNERS OUTLOOK Welcome to the band new Patnes Outlook newslette. It s had to believe it s June and anothe end of financial yea is aleady ceeping up.
More informationCollege Enrollment, Dropouts and Option Value of Education
College Enollment, Dopouts and Option Value of Education Ozdagli, Ali Tachte, Nicholas y Febuay 5, 2008 Abstact Psychic costs ae the most impotant component of the papes that ae tying to match empiical
More information