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1 r Campbell Williams, Inc. Private Investor Services An Overview of Modern Portfolio Theory and Prudent Investment Strategies Campbell Williams, Inc. is Registered Investment Advisor with the State of Florida Page 1
2 In the 1950 s, Prof. Harry Markowitz decided to explore the effects of risk on portfolios of securities. He felt that there was a reasonable understanding of return, but the interaction of risk and return was not so clear. Together with two others academics, he later won a Nobel Price for development of Modern Portfolio Theory. Prof. Markowitz started by looking at a lot of portfolios charted by their Return and Risk characteristics as below. Each green dot is a portfolio of various securities. Each portfolio has a specific return on the left axis (expected or historical) and a risk factor on the bottom axis. Risk is represented as Standard Deviation. Let s have a mini refresher course on Standard Deviation, before we continue with Modern Portfolio Theory. Understanding The Efficient Frontier Expected Return Possible Portfolios 8% Risk (Standard Deviation) Page 2
3 Standard Deviation is used in statistical analysis. We use it to understand volatility of securities prices and portfolio value. Below is a graph showing the PRICE CHANGE of a stock from year to year (as its Percent Change from Prior Year). In Year 1, the price of the stock was BELOW the price of the stock the year before, i.e. -. In Year 2, the price of the stock was 1 ABOVE the price in Year 1, i.e And the pattern continues in our simple example - then + 1 from year to year. STANDARD DEVIATION: Annual Price Change of Investment A PERCENT CHANGE FROM PRIOR YEAR 1 - Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Page 3
4 When we calculate the AVERAGE Annual Price Change, it is. STANDARD DEVIATION: What is the Average Price Change of Investment A? PERCENT CHANGE FROM PRIOR YEAR 1 - Average Annual Price Change Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Page 4
5 When we study the AVERAGE compared to the percent change each year, we note that: - there is a movement or spread or deviation AROUND the Average, i.e., above and below the Average. The statisticians use the term Deviation (and technically use the term Mean instead of Average). In our simple case, this security has a Standard Deviation of from the Mean. It goes up and down AROUND the Average return. STANDARD DEVIATION: What is the Deviation from the Average of Investment A? PERCENT CHANGE FROM PRIOR YEAR Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Page 5
6 Now let s look at the history of the S&P 500 Index - the Standard & Poors record of Annual Returns of the 500 largest companies in the U.S. in various industries. The Graph below shows 20 + years of history of the Annual Return each year. In 1972, the value of the 500 companies stocks grew 19%. In 1973, the value decreased 1, and in 1974 it decreased another 26%, etc. Most people are not aware that the volatility shown in the graph is common - in many types of securities, in the U.S. and other countries. Institutional investors focus on how to deal with this volatility issue. Modern Portfolio Theory helps deal with this problem, as you will see. Annual Return of S&P 500 S&P 500 Annual Return % 3 32% 32% 31% 3 Annual Return % 2 19% 24% 7% 18% 21% 23% 6% 18% 17% 7% - 1% % % % -3 Page 6
7 We can put the Annual Return data into the computer and calculate the AVERAGE Annual Return over the years shown. The AVERAGE is 12.3% for this period. AND, the computer calculates the Standard Deviation as 16.. When we look at the next slide, Standard Deviation of S&P 500 S&P 500 Annual Return Average Annual Return 5 4 Standard Deviation of 16. from the Average 37% 3 32% 32% 31% 3 Annual Return 2 19% 24% 21% 23% 18% 18% Average Annual Return 12.3% 7% 6% 17% 7% - 1% % % % -3 Page 7
8 ... we can see clearly what the 16. Standard Deviation really means: If we ADD 16. to the AVERAGE of 12.3%, we get % - the top of the black vertical bars. If we SUBTRACT 16. from the AVERAGE of 12.3%, we get - 4.2% - the bottom of the black vertical bars. Technically, this band of - 4.2% to % is ONE Standard Deviation: 6 of the time, the Annual Return is within this band. As you can see, about 1/3rd of the points are above or below the band! Standard Deviation of S&P 500 S&P 500 Annual Return Average Annual Return 5 One Standard Deviation: +/ % 32% 32% 31% +28.8% 3 Annual Return 2 19% 24% 7% 18% 4 21% 23% 6% 18% 17% 12.3% 7% % % -4.2% 1% % -3 Page 8
9 The slide below shows TWO Standard Deviations -which includes 9 of the points (only one observation is outside the band) - and is 33.1% added to or subtracted from 12.3%. So, we are looking at fluctuation AROUND the Average Return of between +4 and -21%. We will be using both One and Two Standard Deviations when looking at possible portfolios, to better understand the Probable Risk. And we will be constructing portfolios which ANTICIPATE the probable volatility of its different component asset classes. And you will see how managing this volatility inherent in securities can be aided by on-going use of Modern Portfolio Theory tools. Standard Deviation of S&P S&P 500 Annual Return Average Annual Return Two Standard Deviations: +/- 33.1% +45.4% 4 37% 3 32% 32% 31% 3 Annual Return 2-24% 21% 23% 19% 18% 18% 17% 7% 6% 12.3% 7% 1% % % % -20.8% Page 9
10 Back to Prof. Markowitz... and his Efficient Frontier concept. The Professor s first step was: let s select a specific risk level, say Standard Deviation. Then, which portfolio has the highest return for that level of risk? Expected Return 8% Understanding The Efficient Frontier 2 1 Which portfolio has the highest return? At this level of RISK Risk (Standard Deviation) Page 10
11 The answer is obvious.... And we now understand that the portfolio is Expected to have a Standard Deviation around an average total return over time of 8%. Understanding The Efficient Frontier At this level of RISK Expected Return 8% This portfolio has the highest possible return! Risk (Standard Deviation) Page 11
12 Prof. Markowitz called this portfolio with the highest return the Efficient Portfolio for this particular level of risk. Having tried different proportions of the types of investments included in the mixer, there is only one combination which gives the highest return. Who would want a portfolio with less return for the same risk? So the goal of an Institutional Investor is to always have an Efficient Portfolio! Understanding The Efficient Frontier So this is an Efficient Portfolio Expected Return 8% Risk (Standard Deviation) Page 12
13 At each level of risk (Standard Deviation), only one portfolio has the highest return - i.e., the Efficient Portfolio for that level of risk. You can also see that the old saying is clear:... the higher the risk, the higher the return. Understanding The Efficient Frontier Expected Return 8% And these are all Efficient Portfolios for different levels of Risk Risk (Standard Deviation) Page 13
14 The other portfolios, now shown in red, Prof. Markowitz called Inefficient Portfolios... less return for the same risk. There are no portfolios above the Efficient Portfolio, because there are no combinations of the assets we are working with which would produce a higher return at any specific risk level. Expected Return 8% Understanding The Efficient Frontier Since Efficient Portfolios have the highest possible return, there are And these are Inefficient Portfolios Risk (Standard Deviation) Page 14
15 Prof. Markowicz then suggested that we consider this series of portfolios as a continuous line of all the Efficient Portfolios. and he created the term Understanding The Efficient Frontier Expected Return The line through all the Efficient Portfolios... 8% Risk (Standard Deviation) Page 15
16 Efficient Frontier Since there are no portfolios beyond (above) this line, it makes sense. Understanding The Efficient Frontier Expected Return... is the Efficient Frontier 8% Risk (Standard Deviation) Page 16
17 However, there is not just ONE Efficient Frontier! There are different Efficient Frontiers depending on what types of assets were allowed to be included in the mixing process. For instance, venture capital or emerging market stocks or municipal bonds may not have been used in the portfolio mix. The Efficient Frontier will change when you add or take away types of assets or limit how much of the portfolio can be invested in one type of asset. Understanding The Efficient Frontier Expected Return or more correctly, the Efficient Frontier... 8%... for a specific group of assets. Risk (Standard Deviation) Page 17
18 The graph below shows actual Efficient Frontiers. The lower, MAGENTA line is an Efficient Frontier if only certain types of bonds are included in the portfolio. The middle, BLUE Efficient Frontier includes some bonds and some types of equities. The top, GREEN Efficient Frontier includes more types of bonds and equities. So, for the same level of risk, say 7%, different Efficient Frontiers can result in different return. There can be several Efficient Frontiers... 12%... depending on the asset classes allowed. 11% ANNUAL RETURN 9% 8% 7% 6% Many Equity & Fixed Income Asset Classes Several Equity & Fixed Income Asset Classes Fixed Income Asset Classes Only 4% 2% 4% 6% 8% 12% 14% 16% 18% 2 RISK (Standard Deviation) Page 18
19 Professor Markowitz also focused on the correlation of price movements of individual securities, or groups of securities, within a portfolio. In the chart below, we can see that the annual return of A and B move exactly together. They are highly correlated to each other. (a value of +1 is perfect) On the other hand, A hand C move in exactly opposite, mirror, directions. They are negatively correlated. (a value of -1 ) By combining components with low correlation, or with no correlation, volatility is significantly reduced or dampened. So, assets with higher returns and higher standard deviation can be combined and result in a constructed portfolio with higher return and much less volatility than the individual components - if there is poor correlation among the investments. CORRELATION: A and B... have high correlation. A and C... have negative correlation. ANNUAL RETURN B A C B A C Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Page 19
20 In the graph below, we show the volatility of Total Return of several different types of investments or asset classes. The RED line is the same S&P 500 index, which we saw before. The BLACK line is longer term Treasury Bonds of the U.S. Government. Remember the 1980 s? When interest rates fluctuate, the value of bonds change. The BROWN line is U.S. small company stocks - good return, but quite volatile! Note that many years have positive total returns of 20 percent or more and other years have negative total returns of -10 percent or more. This is the real world. Institutional Investors focus on managing the risks of this volatility, with the help of Professor Markowitz. Dampening Volatility Risk with an Efficient Portfolio ANNUAL RETURN T-Bonds S & P 500 Ann. Return Small Co. Ann % -4-6 Page 20
21 In this case, we have added the BLUE line of International Equities, composed mainly of the equities of large companies in the developed countries, and a small portion of Emerging Market Equities. (The index is the EAFE - Europe, Australia, and Far East prepared by Morgan Stanley.) Note that the volatility is high, but the correlation to the S&P 500 (red line) is not too great. They are often moving differently. Dampening Volatility Risk with an Efficient Portfolio ANNUAL RETURN T-Bonds S & P 500 Ann. Return Small Co. Ann % EAFE Ann. Return -6 Page 21
22 The BROAD DARK BLUE line added here, is a constructed Moderate Portfolio, having moderate return and moderate risk. You will notice, that in most years it was substantially less volatile than the various asset classes. When all or most asset classes are up or down, it is also more volatile - but less so than most of the individual asset classes. There are two goals in trying to dampen or flatten the volatility of the portfolio: 1. To minimize the change in the value of the portfolio, for the psychological benefit of the investor; and 2. A less volatile portfolio arithmetically compounds more effectively over time than a more volatile portfolio with the same average return. Focus should be on increasing the average return over time by ½ of 1% or 1%, cutting through the major swings of or 2 or 3 in many asset classes. Dampening Volatility Risk with an Efficient Portfolio ANNUAL RETURN T-Bonds S & P 500 Ann. Return Small Co. Ann % EAFE Ann. Return Moderate Efficient Portfolio -6 Page 22
23 If we had invested $100,000 at the beginning of the period, in each of the asset classes and in the Moderate Portfolio, we would have portfolio growth results below. On several occasions, one asset class grew faster than the Moderate Portfolio. But, it then flattened out (Small ) or went down (EAFE). The Moderate Portfolio grew more consistently than the individual asset classes. Note the results of the Moderate Portfolio compared to the S&P 500. It has grown to twice the size the result of a consistently higher average return over time. So, aggressive investors trying to beat the S&P 500 may not be focusing on the right issues. Institutional Investors have shown that Effective Diversification is very important. Managing risk is key to improving return over time with the benefit of compounding. $2,500,000 And the Moderate Efficient Portfolio Compounds More Effectively Than Individual Asset Classes Growth of $100,000 from 1972 to 1994 $2,000,000 $1,500,000 $1,000,000 Moderate EAFE Small Co. S & P 500 T-Bonds $500,000 $ Page 23
24 If we look at several constructed portfolios, compared to the S&P 500 or long term government bonds, we see that even the Defensive Portfolio outperformed the S&P 500. Which of the constructed portfolios do you think had the same standard deviation as the S&P 500? The Aggressive Portfolio is the only one which had a standard deviation as high as the S&P 500. And the Aggressive Portfolio grew to about three times the value of the S&P 500 portfolio. So, an investor could have done considerably better than the S&P 500 with considerably less volatility, or could have done much much better with the same level of risk as the S&P 500. These are just examples of constructed portfolios, to demonstrate that the principles of Modern Portfolio Theory should be used in constructing all portfolios. The Several Efficient Portfolio Historical Examples $3,500,000 Growth of $100,000: December 1971 through December 1994 $3,000,000 $2,500,000 $2,000,000 $1,500,000 Aggressive Moderate Conservative Defensive S & P 500 T-Bills $1,000,000 $500,000 $ Page 24
25 Below is the actual composition of each of the constructed portfolios. You will note that the Moderate Portfolio does not contain super-aggressive asset classes such as Venture Capital. It has 3 in cash and bonds (although most is in Corporate Bonds which have a higher return). And it has 3 in International - mostly in Large Companies, but a portion in Small Companies. Since these asset classes are not highly correlated with the U.S. markets, these investments help to dampen the volatility of the U.S. investments. And the International Small, which is quite volatile on its own, provides high return which improves the overall portfolio average return... while its volatility is dampened by the U.S. investments. Again, these portfolios are just examples - to demonstrate that portfolios constructed using the principles of Modern Portfolio Theory are effective at improving return and moderating risk. Composition of Model Historical Portfolios U.S. Large 1 Defensive International Large Money Market One-year Corporate 3 International Large 2 Conservative International Small Money Market One-year Corporate 2 Five-year Government 4 U.S. Small U.S. Large 2 Five-year Government 2 Moderate Aggressive International Large 2 International Small U.S. Small Money Market U.S. Large 2 One-year Corporate 2 Five-year Government International Large 2 International Small 2 Money Market U.S. Small 1 One-year Corporate U.S. Large 2 Reinhardt, Werba, and Bowen 1996 Page 25
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