Question

Consider a Treasury bill with a rate of return of 5% and the following risky securities: Security

Security A: E(r)= 0.15; variance= 0.400
Security B: E(r)= 0.10; variance= 0.0225
Security C: E(r)=0.12; variance= 0.1000
Security D: E(r)=0.13; variance= 0.0625


The investor must develop a complete portfolio by combining the risk-free asset with one of the securities mentioned above. The security the investor should choose as part of her complete portfolio to achieve the best CAL would be:

a. security D
b. security C
c. security A
d. security B

Answer 1

Security D is likely to be the best choice for combining with a risk-free Treasury bill to achieve the best Capital Allocation Line because it has a high expected return and a lower variance relative to its return. Risky investments like stocks offer higher average returns over time, which compensates for their higher risk compared to bonds and savings accounts.

Step-by-step explanation:

To determine which security to combine with a risk-free Treasury bill for the best Capital Allocation Line (CAL), we need to consider the expected return and variance of the securities. The CAL can be represented by the investment combination that provides the highest expected return per unit of risk. The risk-free rate is 5%, and we have four securities to choose from:

Security A: Expected return (E(r)) = 15%; Variance = 0.40

Security B: Expected return (E(r)) = 10%; Variance = 0.0225

Security C: Expected return (E(r)) = 12%; Variance = 0.10

Security D: Expected return (E(r)) = 13%; Variance = 0.0625

To decide which security to choose, we look at the Sharpe ratio, which is the measure of the excess return per unit of risk. Without calculating the exact Sharpe ratios, we can compare the risk-return profiles. Based on the given data, the answer is Security D, because it has a relatively high expected return and a lower variance compared to securities with a higher expected return, indicating a potentially better Sharpe ratio. Therefore, an investor looking for the best CAL would likely choose Security D to combine with the Treasury bill.

Investment Risks and Returns

Risky investments traditionally have higher expected returns to compensate for the additional risk. While it is a common misconception that high risk always equates to low returns, it's not accurate. High risk means there is a broader range of possible outcomes, which can include high returns as well. Over time, stocks typically yield higher average returns when compared to bonds and savings accounts, due to the higher risk investors assume. However, with increased risk comes the potential for greater reward as well as greater loss.

Answer 2

b. security C

Step-by-step explanation:

Risk averse investors are investors that are not risk takers or are risk averse and so from the above, such investors will go for a less variable portfolio which has less risk. The security with the least risk from the options is option B. This is the security that the risk averse investor will choose to add to the portfolio with the risk free t bill