Chapter 12: Portfolio Selection and Diversification Copyright © Prentice Hall Inc Author: Nick Bagley Objective To understand the theory of personal portfolio selection in theory and in practice

Chapter 12 Contents 12.1 The process of personal portfolio selection 12.2 The trade-off between expected return and risk 12.3 Efficient diversification with many risky assets

Objectives To understand the process of personal portfolio selection in theory and practice

Introduction How should you invest your wealth optimally? –Portfolio selection Your wealth portfolio contains –Stock, bonds, shares of unincorporated businesses, houses, pension benefits, insurance policies, and all liabilities

Portfolio Selection Strategy There are general principles to guide you, but the implementation will depend such factors as your (and your spouse’s) –age, existing wealth, existing and target level of education, health, future earnings potential, consumption preferences, risk preferences, life goals, your children’s educational needs, obligations to older family members, and a host of other factors

12.1 The Process of Personal Portfolio Selection Portfolio selection –the study of how people should invest their wealth –process of trading off risk & expected return to find the best portfolio of assets & liabilities Narrower dfn: consider only securities Wider dfn: house purchase, insurance, debt Broad dfn: human capital, education

The Life Cycle The risk exposure you should accept depends upon your age Consider two investments (rho=0.2) –Security 1 has a volatility of 20% and an expected return of 12% –Security 2 has a volatility of 8% and an expected return of 5%

Price Trajectories The following graph show the the price of the two securities generated by a bivariate normal distribution for returns –The more risky security may be thought of as a share of common stock or a stock mutual fund –The less risky security may be thought of as a bond or a bond mutual fund

Interpretation of the Graph The graph is plotted on a log scale in so that you can see the important features The magenta bond trajectory is clearly less risky than the navy-blue stock trajectory The expected prices of the bond and the stock are straight lines on a log scale

Interpretation of the Graph Recall the log scale: the volatility increases with the length of the investment You begin to form the conjecture that the chances of the stock price being less than the price bond is higher in earlier years

Generating More Trajectories This was just one of an infinite number of trajectories generated by the same 2 means, 2 volatilities, and the correlation –I have not cheated you, this was indeed the first trajectory generated by the statistics –the following trajectories are not reordered nor edited Instructor: On slower computers there may be a delay

…and Lots More!

Odd Behavior The top slide has some odd behavior between years 20 and 25 –The price of the stock and bond track each other quite closely, and then they separate, and both end up at 40-years close the their expected prices

From Conjecture to Hypothesis You are probably ready to make the hypothesis that –the probability of the high-risk, high-return security will out-perform the low-risk, low- return increases with time

But: I promised to be perfectly frank and honest (pfah) with you about the ordering of the simulated trajectories The next trajectory truly was the next trajectory in the sequence, honest!

Explanation The bond and the stock end up at about the same price, when the expected prices are more than a magnitude apart There is either a very good explanation for this, or there is a very high probability that I have been much less than perfectly frank and honest with you

Another View of the Model A little mathematics, and we are able to generate the following price distributions for the stock and the bond for 2, 5, 10, and 40 years into the future

There is a lot going on here, so we will further constrain our view First look at stock prices over a period of 10 years The prices are distributed according to the lognormal distribution

Note –the scale is $0 to $800 –the distribution diffuses and drifts towards higher prices with time –the diffusion is more pronounced in the earlier years than in the later years –you may see that the mode, median, and mean appear to drift apart with time

Bond in Time You will recall that if you invest in a 5-year default-free pure discount bond for 5 years, the return is known with certainty To avoid this effect, assume we invest in short term bonds, and roll them over as they mature

Note –the scale is now $0 to $400 (not $0 to $800 as in the case of the stock) –we observe the same kind of diffusion and drift behavior, and there is less of each (remember to adjust for the scale)

Contrast of Trajectories and Distributions The price distributions and the trajectories were generated from the same distribution. But They do not seem to agree –The distributions appear to produce much lower averages (expected returns) than the trajectories

Meaty Tails The resolution is that the distributions have much meatier tails than your intuition allows, pushing the median and mean further and further from the mode with time The region where the left tail appears to have drifted into insignificance has a profound affect on the mean

Stock and Bonds Distributions Compared at the Same Times The next sequence of slides contrasts the distribution of stock and bond prices at 1, 2, 5, 10, and 40 into the future Some of the slides have different measures of central tendency indicated Note the behavior of these statistics as time increases

Mode =104Mode =106Median=104Mean =104Median=111Mean = 113

Mode = 122Mode = 135Median= 126 Mean = 128Median= 165 Mean = 182

Mode =503Mode =1,102Median=650Mean =739Median=5,460Mean =12,151