Question

1. Short Answer Questions: John is considering investing in the stock market. He has studied FIN3000 at Baruch College, so he has a rough idea that diversification is good. He decides to create a portfolio with 80% of his wealth in Stock A (beta=0.2; std. = 15%) and 20% of his wealth in Stock B (beta=1.5; std. = 12%). The reason why he puts much higher weight in Stock A is because he believes that the low beta value of Stock A can lead him to lower risk. Please comment on his thought. Is there anything wrong with John’s reasoning? How would you suggest him to conduct his financial decision?

(Note: There is a model answer for the part reasoning why John is right or wrong. However, there is no model answer for the suggestion part. In the real final exam, I will grade questions like this based on 2 criterions: first, does your suggestion follow the right concept we learned in the class? And second, how far and decent you can elaborate.)

Answer 1

John is wrong in his approach.

MEASURES OF RISK

There are two types of risk, systematic and unsystematic risk. Systematic risk affects the entire stock market. The recession of '08 is a good example of systematic risk. It affected all stocks. On the other hand, unsystematic risk is risk that only affects a particular security. For example, the risk of Tesla declaring bankruptcy is an unsystematic risk. It does not affect the entire market.

Unsystematic risk can be eliminated with a well-diversified portfolio. But basically, by holding enough uncorrelated securities, unsystematic risk can be eliminated. However, if investors were compensated for taking risk that can be eliminated, the return of unsystematic risk would be arbitraged to zero. Therefore, investors are only compensated for systematic risk.

This is where beta and standard deviation come in. Standard deviation represents total risk, the sum of systematic and unsystematic risk (i.e., the sum of variances). Beta measures systematic risk only, which is what return should be based on in an efficient market. Assuming you have a well-diversified portfolio, you are more focused on the systematic risk of a security because that is what returns are based on. Therefore, you look at beta to measure risk/return. However, if you have no portfolio to start with, unsystematic risk is more relevant to you. In this case, standard deviation is your friend because it accounts for both risk types.

With just two stocks, there are little chances of effective diversification in the portfolio (it depends upon the correlation coefficient between the two stocks).

Hence, standard deviation is the appropriate measure of risk in this case.

For a two-asset portfolio, the expected return and risk (or standard deviation) of the portfolio is given by:

The optimal way of choosing the proportion of the two stocks in the portfolio is to maximize the Sharpe ratio of the portfolio, which is given by:

Sharpe ratio = [E(Rp) - Rf] / σp