Question

Abraham, Bernie, and Cecilia are Sharpe ratio maximisers. Having analysed all the companies on the stock market, they have uniform expectations on the future returns of all stocks, their volatilities, and the correlations between all the stocks. Based on this information, they have estimated that the expected return on the portfolio that maximises the Sharpe ratio is 6,8 per cent with a volatility of 23,1 per cent. The risk-free rate of return is 2 per cent. However, the persons are not uniform in their personal risk preferences.

The risk aversion coefficients are the following:
a)Abraham's risk aversion coefficient is 4. Let us call Abraham Person 1.
b)Bernie's risk aversion coefficient is 8. Let us call Bernie Person 2.
c)Cecilia's risk aversion coefficient is 3,2. Let us call Cecilia Person 3.
d)What is the Sharpe ratio of Person 2's portfolio?

Answer 1

The Sharpe ratio for Bernie's (Person 2) portfolio is approximately 0.2078, which is calculated by subtracting the risk-free rate from the expected return and dividing by the volatility of the expected return.

Step-by-step explanation:

The Sharpe ratio is a measure used to evaluate the risk-adjusted return of an investment portfolio. The Sharpe ratio of a portfolio can be calculated using the expected return on the portfolio, the risk-free rate of return, and the volatility (standard deviation) of the portfolio’s excess return. In the question presented, Bernie (Person 2) is a Sharpe ratio maximiser with a risk aversion coefficient of 8. However, the risk aversion coefficient does not directly affect the Sharpe ratio calculation. Therefore, since all three individuals (Abraham, Bernie, Cecilia) have uniform expectations and given the same data, the Sharpe ratio for each person's portfolio would be the same.

To calculate the Sharpe ratio, we subtract the risk-free rate from the expected return, then divide it by the portfolio's volatility:

Sharpe Ratio = (Expected Return - Risk-Free Rate) / Volatility

For Person 2's portfolio, the calculation would be:

Sharpe Ratio = (6.8% - 2%) / 23.1%

Sharpe Ratio = 4.8% / 23.1%

Sharpe Ratio ≈ 0.2078