Question

You are considering the risk-return of two mutual funds for investment. The relatively risky fund promises an expected return of 14.7% with a standard of 15.6%. The relatively less risky fund promises an expected return and standard deviation of 6.4% and 3.8%, respectively. Assume that the returns are approximately normally distributed. Using normal probability calculations and complete sentences, give your assessment of the likelihood of getting, on one hand, a negative return and on the other, a return above 10% with these funds. You may choose to use excel normal distribution formulas, but if you do, give the explicit formulas. Offer some remarks about your possible investment approach.

Answer 1

Assumining that the investments are independent.

we have

...............using absolute terms

We want to know the probability of collectively making a negative return or above 10%. These two events are independent so we will add these probabilities.. We will need a distribution of their sums

Let Z = X1 + X2

Means E(Z) =

= 21.1

For std dev we first add the variances and then take their square root. This is the formula for two random variables sum

V(Z) =

= 257.8

S(Z) = 16.056

Therefore the distribution of 'Z' is

z-score = .............z' is to distinguish from std normal.

We will use the std normal probability tables

P(Z < 0) + P(Z > 10) = P(Z-score < -1.31) + P(z-score> -0.69)

= 1 - P(z-score < 1.31) + P(z-score < 0.69)

= 1 - 0.9056 + 0.75532

Probability = 0.84972