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Chapter 5: Problem 11

A moderately risk-averse investor has 50 percent of her portfolio invested in stocks and 50 percent in riskfree Treasury bills. Show how each of the following events will affect the investor's budget line and the proportion of stocks in her portfolio: a. The standard deviation of the return on the stock market increases, but the expected return on the stock market remains the same. b. The expected return on the stock market increases, but the standard deviation of the stock market remains the same c. The return on risk-free Treasury bills increases.

Short Answer

Expert verified
In summary, an increase in standard deviation (or risk) results in a steepened budget line and possibly a decreased proportion in stocks, an increase in expected return results in an upward shift of the budget line and possibly an increased proportion in stocks, and an increase in risk-free return results in a higher starting point of the budget line and possibly a decreased proportion in stocks.

Step by step solution

01

Effect of Increase in Standard Deviation

In financial terms, standard deviation represents risk. Therefore, if the standard deviation of the return on the stock market increases with the expected return remaining the same, this implies that the risk associated with stock investment increases while the potential return is unchanged. In response to this change, the budget line of the investor steepens because the potential risk (i.e., the cost) associated with each additional unit of potential return increases. This might cause the investor to reduce the proportion of stocks in her portfolio due to her risk-averse nature.
02

Effect of Increase in Expected Return

When the expected return on the stock market increases and the standard deviation remains the same, this means that the potential gain from stock investment becomes greater while the risk remains unchanged. Consequently, the budget line of the investor shifts upwards to reflect higher potential returns at each level of risk. Given this change, the investor might increase the proportion of stocks in her portfolio due to higher expected returns.
03

Effect of Increase in Risk-Free Return

If the return on risk-free treasury bills increases, this implies that the investor can earn a higher return without taking on any additional risk. This shifts the starting point of the budget line upwards, while the slope (representing the trade-off between risk and return) does not change. Given her risk-averse nature, the investor would likely increase the proportion of her portfolio invested in risk-free asset and decrease the proportion in stocks.

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Most popular questions from this chapter

Suppose you have invested in a new computer company whose profitability depends on two factors: (1) whether the U.S. Congress passes a tariff raising the cost of Japanese computers and (2) whether the U.S. economy grows slowly or quickly. What are the four mutually exclusive states of the world that you should be concerned about?

As the owner of a family farm whose wealth is \(\$ 250,000,\) you must choose between sitting this season out and investing last year's earnings \((\$ 200,000)\) in a safe money market fund paying 5.0 percent or planting summer corn. Planting costs \(\$ 200,000,\) with a six-month time to harvest. If there is rain, planting summer corn will yield \(\$ 500,000\) in revenues at harvest. If there is a drought, planting will yield \(\$ 50,000\) in revenues. As a third choice, you can purchase AgriCorp drought-resistant summer corn at a cost of \(\$ 250,000\) that will yield \(\$ 500,000\) in revenues at harvest if there is rain, and \(\$ 350,000\) in revenues if there is a drought. You are risk averse, and your preference for family wealth (W) is specified by the relationship \(U(W)=\sqrt{W} .\) The probability of a summer drought is \(0.30,\) while the probability of summer rain is 0.70 Which of the three options should you choose? Explain.

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