Question

Q. Mr. Miles is a first time investor and wants to build a portfolio using only U.S. T-bills and an index fund that closely tracks the S&P 500 Index. The T-bills have a return of 5%. The S&P 500 has a standard deviation of 20% and an expected return of 15%.

1. Draw the CML and mark the points where the investment in the market is 0%, 25%, 75%, and 100%.

2. Mr. Miles is also interested in determining the exact risk and return at each point

Answer 1

1) The equation for CML is calculated as E(R_p) = 5% + 0.50 x _p by substituting the given information into general CML Equation. The intercept of the line is 5%, and its slope is 0.50. CML can be drawn by taking ant two points on the line that satisfy the above equation.

Alternatively, CML can also be drawn by connecting risk-free return of 5% on the y-axis with the market portfolio at (20%, 15%). The CML is shown in below diagram -

2) Return with 0% invested in Market = 5%, which is risk free return.

Standard deviation with 0% invested in market = 0% because T-Bills are not risky.

Return with 25% invested in market = (0.75 x 5%) + (0.25 x 15%) = 7.5%

Standard deviation with 25% invested in market = 0.25 x 20% = 5%

Return with 75% invested in market = (0.25 x 5%) + (0.75 x 15%) = 12.5%

Standard deviation with 75% invested in market = 0.75 x 20% = 15%

Return with 100% invested in market = 15%, which is the return on S&P 500.

Standard deviation with 100% invested in market = 20%, which is the risk of S&P 500.