# A. What is the expected return and volatility (standard deviation) of your investment? b. What is your realized return if J goes up 25% over the line? c. What return do you realize if J falls by 20% over the year?

Suppose you have \$100,000 in cash, and you decide to borrow another \$15,000 at a 4% interest rate to invest in the stock market. You invest the entire \$115,000 in a portfolio J with a 15% expected return and a 25% volatility.

a. What is the expected return and volatility (standard deviation) of your investment?

b. What is your realized return if J goes up 25% over the line?

c. What return do you realize if J falls by 20% over the year?

#### Solution Preview

... of investment= w1 r1 + w2 r2
and volatility (standard deviation) of investment= w1 s1 as other terms with s2 drop out of the equation since s2=0

w1= proportion invested in portfolio J, w2 = proportion borrowed
r1= return on J, r2 = interest rate on borrowing
s1= standard deviation of return on J, s2= standard deviation of interest rate on borrowing=0

own cash= \$100,000
amount borrowed= \$15,000
Total invested in J= \$115,000

w1= 1.15 ...