Question

You've just decided upon your capital allocation for the next year. You believe the expected return should be 10% and the standard deviation is 28%. The risk-free rate is 5%. As the market moves, you would like to raise the expected return, lower the standard deviation of your risky portfolio, and adjust the risk-free rate to 4%.  

a)Will you increase or decrease your allocation in the risky portfolio given the same expected return?

b) When the risk-free rate increases from inflation, should investors reduce their allocation to the risky portfolio given the same expected return? Why? Please use the diagrams in your answer.

Answer 1

Sharpe ratio (SR) is a measure of performance of a stock/portfolio/investment adjusted for total risk, represented by . Higher the Sharpe ratio, better is the investment.

Formula: Sharpe Ratio = (E(R) - Rf) /

Following are inferences from the SR formula:

Parameter	Increase/Decrease	Impact on SR	Overall relation with SR
E(R)	Increases	Increase	Positive
Rf	Increases	Decrease	Negative
	Increases	Decrease	Negative

Therefore, basis the given data,

SR = (10% - 5%) / 28%

SR = 0.1786

As the market moves, E(R) is expected to increase and is expected to be lowered as well as Rf is expected to be lowered. Therefore, using the above relations, impact on SR is as follows:

Parameter	Increase/Decrease		Overall relation with SR	Impact on SR
E(R)	Increases		Positive	Increase
Rf	Decrease		Negative	Increase
	Decrease		Negative	Increase

a) As Sharpe ratio is likely to increase as the market moves, allocation to the risky portfolio can be increased in order to earn a high risk adjusted return from the portfolio.

b) If risk free rate increases (keeping all the factors constant), the Sharpe ratio is likely to decline, since Rf has a negative relation to SR (using relations from table above). Therefore, investors reducing their allocation is correct step since they are trying to avoid the lower risk adjusted return.