Question

Suppose you have some money to invest-for simplicity, $1-and are planning to put a fraction w into a stock market mutual fund and the rest ( 1− w ), into a bond mutual fund. Suppose that a $1 invested in a stock fund yields ??after one year and a $1 invested in a bond fund yields Rb . ?? and Rb are random variables with expected value of 9% and 7% respectively, and standard deviation of 4% and 2% respectively. The correlation between ?? and Rb is 0.75. If you place a fraction w of your money in the stock fund and the rest ( 1− w ), in the bond fund then the return on your investment will be R wRs w Rb = + (1− ) . The risk associated with your investment is measured by the standard deviation. a. If you decide to invest 60% of your $1 in stock and the rest in bond, then what is the expected return of your investment? What is its associated risk? B. What share of your $1 money should you invest in stock in order to expect a 8.6% return on your investment? For that same share i.e. invested in stock, what level of risk is associated with your investment? C. What share of your $1 money should you invest in stock mutual fund in order for your investment risk to be 3%? (you can show your work using algebra, or calculus).

Answer 1

Answer:

Given that:

Supposen you have some money to invert - for simplicity ,$1 and are planning to put a fraction w into a stock mutual fund and the rest (1-w) , into a bond mutual fund.

a)

  Expected Return = Weight of Stock Return on Stock + Weight of Bond Return on Bond

Expected Return = 60% 9% + 40% 7%

Expected Return = 8.20%

Associated Risk = Sqrt(Weight of Stock^2 Risk on Stock^2 + Weight of Bond^2 Risk on Bond^2 + 2 Weight of Stock Weight of Bond risk of Stock risk of bond * correlation)

Associated Risk = Sqrt(0.60^2 0.04^2 + 0.40^2 0.02^2 + 2 0.60 0.40 0.04 0.02 * 0.75)

Associated Risk = Sqrt(0.000576 + 0.000064 + 0.000288)

Associated Risk = Sqrt(0.000928)

Associated Risk = 0.0305 or 3.05%

b)

  Expected Return = Weight of Stock Return on Stock + Weight of Bond Return on Bond

8.60% = Weight of Stock 9% + (1 - Weight of Stock) 7%

8.60% = Weight of Stock 9% + 7% - 7% Weight of Stock

1.60% = 2% * Weight in Stock

Weight of Stock = 80%

Weight of Bond = 1 - Weight of Stock = 1 - 80% = 20%

Associated Risk = Sqrt(Weight of Stock^2 Risk on Stock^2 + Weight of Bond^2 Risk on Bond^2 + 2 Weight of Stock Weight of Bond risk of Stock risk of bond * correlation)

Associated Risk = Sqrt(0.80^2 0.04^2 + 0.20^2 0.02^2 + 2 0.80 0.20 0.04 0.02 * 0.75)

Associated Risk = Sqrt(0.001024+ 0.000016+ 0.000192)

Associated Risk = Sqrt(0.001232)

Associated Risk = 0.0351 or 3.51%

c)

by using the goal seek function in excel the weight in Stock came to be 58% (associated risk at 58%)

Associated Risk = Sqrt(Weight of Stock^2 Risk on Stock^2 + Weight of Bond^2 Risk on Bond^2 + 2 Weight of Stock Weight of Bond risk of Stock risk of bond * cor relation)

Associated Risk = Sqrt(0.58^2 0.04^2 + 0.42^2 0.02^2 + 2 0.58 0.42 0.04 0.02 * 0.75)

Associated Risk = Sqrt(0.00053824+ 0.00007056+ 0.00029232)

Associated Risk = Sqrt(0.0009)

Associated Risk = 3%