Question

Suppose that Treasury bills offer a return of about 6% and the expected market risk premium is 8.5%. The standard deviation of Treasury-bill returns is zero and the standard deviation of market returns is 20%. Use the formula for portfolio risk to calculate the standard deviation of portfolios with different proportions in Treasury bills and the market. (Note: The covariance of two rates of return must be zero when the standard deviation of one return is zero.) Graph the expected returns and standard deviations.

https://www.chegg.com/homework-help/suppose-treasury-bills-offer-return-6-expected-market-risk-p-chapter-7-problem-22p-solution-9780077356385-exc?hwh_cr=1

Can someone explain from step 3 onwards, as the explanation is too brief.

For step 4, why do we have to add the numbers together (0.06+0.85) . Where is 0.145 coming from?

And isn't this 0.085?

Thanks!

Answer 1

Answer:

I could not access the link you have given. However, I give below the full answer:

Return on treasury bills = 6%

Market rate of return = Risk free rate + Market risk premium = 6% + 8.5% = 14.5%

Further:

As standard deviation of Treasury-bill returns = 0

Standard deviation of Portfolio (of Treasury bills and Market) will be = Standard deviation of market * Proportion of market in portfolio

Calculation of expected return and standard deviation of portfolio at different proportions in treasury bills and market:

Let us calculate expected returns of portfolio with 10% of Treasury Bills and 90% of market = 10% * 6% + 90% * 14.5%

= 13.65%

Standard deviation will be = 20% * 90%= 18%

Similarly we calculate below expected returns and standard deviation with different proportions.

Graph of expected returns and standard deviation: