Question

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

Answer 1

increases and decreases

Step-by-step explanation:

The budget line will become flat and the slope will decrease. The proportion of stocks in the portfolio will fall.

The equation for the budget line is given by,

Rp=((Rm-Rf)/SDm)*SDp + Rj

where Rp is the expected return on the portfolio, Rm is the expected return from investing in the stock market, Rf is the risk-free return on Treasury bills, SDm is the standard deviation of the return from investing in the stock market, and SDp is the standard deviation of the return on the portfolio.

So when the standard deviation of the return on the stock market increases, the slope of the budget line decreases making the budget line to become flatter. The budget line’s intercept stays the same as Rf does not change. As stocks have become riskier without a compensating increase in expected return, the proportion of stocks in the investor’s portfolio will fall.