Consider the following capital market: a risk-free asset yielding 1.50% per year

Question

Consider the following capital market: a risk-free asset yielding 1.50% per year and a mutual fund consisting of 55% stocks and 45% bonds.  The expected return on stocks is 9.00% per year and the expected return on bonds is 2.50% per year.  The standard deviation of stock returns is 23.00% and the standard deviation of bond returns 8.00%.  The stock, bond and risk-free returns are all uncorrelated.

What is the expected return on the mutual fund? What is the standard deviation of returns for the mutual fund? Now, assume the correlation between stock and bond returns is .70 and the correlation between stock and risk-free returns and between the bond and risk-free returns are o (by construction, correlations with the risk-free asset are always zero). What is the standard deviation of returns for the mutual fund? Is it higher or lower than the standard deviation found in part 2? Why? Now, assume that the standard deviation of the mutual fund portfolio is exactly 11.00% per year and a potential customer has a risk aversion coefficient of 2.0 What correlation between the stock and bond returns is consistent with this portfolio standard deviation? What is the optimal allocation to the risky mutual fund(the fund with exactly 11.00% standard deviation) for this investor? What is the expected return on the complete portfolio? What is the standard deviation of the complete portfolio? What is the Sharpe ratio of the complete portfolio?

Explanation / Answer

Bond funds and cash equivalent funds will earn 3% to 5% every year with almost no risk, but 5% sucks for a long term investment.

Good stock based funds can average 12% or more over long periods of time, but they are volatile and will have really good years and really bad years that average out to 12%.

You can get a mutual fund anywhere in between. Some even perform better than 12% but those are even worse for ups and downs.

There are different types of funds that invest in different types of investments. The type of fund you choose will determine what the average return should be in order to be considered good for its category. That's kind of like asking "what's a good amount of horsepower for a car?" It would depend what type of car it was as a 200hp sedan would have tons of power, but 200hp in a full size truck would be horrible, so it depends on the class of vehilce, just like mutual fund returns depend on the type of fund.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.