Solution to Case 02
Risk and Return
Flirting With Risk
1. Imagine you are Bill. How would you explain to Mary the relationship between risk and return of individual stocks?
I would explain to Mary that risk and return are positively related, i.e. if one expects to earn higher returns, then one has to be willing to invest in stocks whose price can vary significantly from year to year or in different economic conditions. For example, in the table below we see that treasury bills would have yielded 4% with almost no variability, while the index fund is expected to yield 10.1% with a standard deviation of 9.15%.
| | Expected Rate of Return | |Scenari/o |Probability |Treasury Bill |Index Fund |Utility Company |High-Tech Company|Counter-Cyclical | | | | | | | |Company | |Recession |20% |4% |-2% |6% |-5% |20% | |Near Recession |20% |4% |5% |7% |2% |16% | |Normal |30% |4% |10% |9% |15% |12% | |Near Boom |10% |4% |15% |11% |25% |-9% | |Boom |20% |4% |25% |14% |45% |-20% | |Expected Return | |4% |10.10% |9.2% |15.40% |5.9% | |Standard Deviation | |0% | |2.82% | |15.69% | | | | |9.15% | |17.69% | |
2. Mary has no idea what beta means and how it is related to the required return of the stocks. Explain how you would help her understand these concepts.
Beta is defined as the systematic risk of an asset. It measures the relationship between the returns of an asset and a market portfolio. Stocks that vary by more than the market have betas greater than 1 and vice-versa. The formula for calculating beta is as follows:
Beta = Covariance of stock returns vis-à-vis market returns Variance of market returns
According to the Security Market Line equation,
Required return on a stock = Risk free rate + (Expected Market Return – Risk free rate)* Beta
This shows that high beta stocks have a have a higher required rate of return than low beta stocks.
Cov (Rs, Rm)
-1.54 Required Rate
*See spreadsheet for calculations
3. How should Bill demonstrate the meaning and advantages of diversification to Mary?
Diversification refers to the strategy of investing in stocks, which are not highly correlated with each other, for example, high-tech firms and utility firms, or high-tech firms and counter-cyclical firms. Diversification reduces the portfolio’s variability and thereby enables investors to earn a more stable rate of return. To demonstrate the advantages of...
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