Question

Given the following information, calculate the risk-adjusted return:

90-day T-bill rate: 4%
Actual return: 14%
Beta = 1.4
CPI (Consumer Price Index): 3%
Standard deviation: 5.0%
Options:
A) 9.4%
B) 10.6%
C) 11.8%
D) 12.2%

Answer 1

To find the risk-adjusted return, subtract the 90-day T-bill rate from the actual return to determine the excess return, then adjust this figure according to the investment's beta. The calculation based on the question's data seems to indicate a 14% risk-adjusted return, which does not match any of the given options.

Step-by-step explanation:

To calculate the risk-adjusted return, you must adjust the actual rate of return on the investment by the risk-free rate of return, which is often represented by the 90-day T-bill rate, and then adjust further for the investment's risk, represented by the beta. In this case, we start with the given actual return of 14% and subtract the risk-free rate of 4%. The result is known as the excess return, which compensates the investor for taking on higher risk compared to the risk-free asset.Our calculation to find the risk premium (excess return) would be:Actual return: 14%Risk-free rate: 4%We subtract the risk-free rate from the actual return:14% - 4% = 10%This 10% is the excess return. But, since we need to adjust for the investment's risk as represented by its beta of 1.4, we take this one step further.

The risk-adjusted return is therefore not just the excess return but the excess return adjusted for the investment's beta.The risk-adjusted excess return is calculated by multiplying the excess return by the beta:10% * 1.4 = 14%Since the T-bill rate is already considered in the excess return, adding it back would not be correct, leaving us with a risk-adjusted return of 14%. However, this contradicts the options provided, so it might indicate a need for further clarification on the calculation method expected or a possible oversight in the provided options.

Answer 2

The risk-adjusted return is typically calculated by subtracting the inflation rate and the risk-free rate from the actual rate of return. Given the information provided, which includes a 90-day T-bill rate of 4%, an actual return of 14%, a CPI of 3%, and no market return, the risk-adjusted return is 7%. None of the options given match the calculated value.

Step-by-step explanation:

To calculate the risk-adjusted return, given the following information: 90-day T-bill rate: 4%, Actual return: 14%, Beta = 1.4, CPI (Consumer Price Index): 3%, and Standard deviation: 5.0%, we can use the Capital Asset Pricing Model (CAPM) which suggests that the expected return of an investment equals the risk-free rate plus a risk premium. The risk-free rate is the return of an investment with no risk of financial loss, like the 90-day T-bill rate. The risk premium is the return in excess of the risk-free rate, which is the product of the investment's beta and the market risk premium (the expected market return minus the risk-free rate).

The formula to calculate the expected return using CAPM is: Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate).

However, the question provided does not include the market return, and instead, it requires us to find the risk-adjusted return. This is often done by adjusting the actual return for the risk-free rate and sometimes for inflation as well. Inflation can erode the purchasing power of money, so adjusting returns for inflation provides a more accurate measure of the 'real' return.

Given that we do not have all the parameters for the CAPM, we will assume that the risk-adjusted return for this purpose means the actual return minus the inflation rate and the risk-free rate: Risk-Adjusted Return = Actual Return - Inflation Rate - Risk-Free Rate.

Therefore, Risk-Adjusted Return = 14% - 3% (CPI) - 4% (90-day T-bill rate) = 7%.

None of the options provided A) 9.4% B) 10.6% C) 11.8% D) 12.2% match the calculated risk-adjusted return of 7%. It is possible that the question may be incomplete or could be asking for a different type of risk-adjusted return that requires additional information or formulas not provided.