Investment Management Assignment Help

Investment Management Assignment Help

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You are consultant for a pension fund. The pension fund is allocating money and considers three institutional investors. The first is a stock investor, the second a long-term government and corporate bond investor, the third is a money market manager.

In your function as the consultant you have done your homework and figured out the following track records: Stock investor Bond investor Money market manager

expected return

standard deviation

20%

30%

12%

15%

8%

-

The pension fund requires 24% return to meet its asset/liability-objectives. The guidelines do not allow borrowing, however you can sell short. You wish to construct a portfolio of only stocks and bonds with an expected return of 24% What are the appropriate portfolio proportions and the resulting standard deviations?

What reduction in standard deviation could you attain if you were allowed to borrow at the risk free rate of 8%?

BKM ch. 8, p. 241 # 8

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Graph Point Q is the stock/bond combination with mean = 24%. Let ws be the proportion of stocks and 1 - ws be the proportion of bonds required to achieve the 24% mean, then: 24% = 20 x ws + 12 x (1-ws) = 12 + 8ws ws = 1.50 1- ws = -0.50 Therefore you would have to sell short an amount of bonds equal to 0.50 of your total funds, invest 1.50 times your total funds in stocks. The standard deviation of this portfolio would be: σQ = [1.502 x 900 + (-0.50)2 x 225 +2 x (1.50) x (-0.50) x 45]0.50 = 44.87% If you were allowed to borrow at the risk free rate of 8%, the way to chaieve the target expected return of 24% would be to invest more than 100% of your funds in the optimal risky portfolio, moving out along the CAL, to the rifht of P, up to R, on the graph. R is the point on the optimal CAL which has the mean of 24%. Using the formula for the optimal CAL we can find the corresponding standard deviation: E(rc) = 8 + 0.4601 σc = 24

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Setting E(rc) = 24 we get σc = 34.78%, which is considerably less than 44.78% Graph What is the portfolio composition of point R on the optimal CAL? The mean of any portfolio along this CAL is: Where y is the proportion invested in the optimal risky portfolio P and rP is the mean of that portfolio, which is 15.61% 24 = 8 + y(15.61 – 8) y = 2.1025 This means that for every $1 of your own funds invested in portfolio p, you would borrow an additional $ 1.1025 and invest it also in portfolio P.

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Single-Index and Multifactor Models Consider the following two regression lines for stocks A and B in the following figure.

Figure 1: Regressions of Stock A and B vs. Market which stock has higher firm-specific risk?

Which stock has greater systematic (market) risk Which stock has higher R2 which stock has higher alpha? which stock has higher correlation with the market?

Problem-statement: Discuss the questions, no analytical solution required. economicshomeworkhelper.com

Solution: BKM ch. 3, p. 314 # 3 The two figures depict the stocks security characteristic lines (SCL) Stock A has a higher firm-specific risk because the deviations from the SCL are larger for A than for B. Deviations are measured by the vertical distance of each observation from the SCL. Beta is the slope of the SCL, which is the measure of systematic risk. Stock B’s SCL is steeper, hence stock B’s systematic risk is greater.

The R2 (or squared correlation coefficient) of the SCL is the ratio of the explained variance of the stock’s return to total variance, and the total variance is the sum of the explained variance plus the unexplained variance (the stock’s residual variance).

Since stock B’s explained variance is higher (its explained variance is β Bσ M , which is greater since its beta is higher, and its residual variance β B 2 σ2 is smaller, its R2 is higher ε B than stock A’s.

Alpha is the intercept of the SCL with the expected return axis. Stock A has a small positive alpha whereas stock B has a negative alpha, hence stock a’s Alpha is larger. economicshomeworkhelper.com

The correlation coefficient is simply the square root of R2 , sto stock’s B correlation with the market is higher.

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