1) A portfolio consists of a Treasury bill with a face amount of $20,000 and 300

Question

1) A portfolio consists of a Treasury bill with a face amount of $20,000 and 300 shares of Portland Corp. stock priced at $70 a share. The expected return on the stock is 12%, with sigma of 38%. The T-bill matures after one year, and its yield is 2.9% Find E(Rp) and s (Rp) of the portfolio. 7.626%, 19.73%

2) You have bought 400 shares of Bangor Company at $25 per share and 600 shares of Lewiston Corporation stock at $16 per share. The s(R) of Lewiston is 0.35 and that of Bangor is 0.45. You have calculated the s (Rp) of this portfolio to be 0.37. What is the correlation coefficient between Lewiston and Bangor? 69.62%

3) You invest $29,000 in Augusta which has E(R) = 12% and s(R) = 40% and $21,000 in Auburn stock which has E(R) = 15% and s(R) = 45%. The correlation coefficient between them is .35. Calculate the expected return and sigma of the portfolio in percentage and in dollars. 13.26%, 34.68% and $6,630, $17,338

4) A portfolio consists of 200 shares of Bath Corporation, worth $80 each and 34 bonds of Bangor, selling at par with coupon at 5%. The sigma of the bonds is 4%, and that of the stock 42%. The expected return on the stock is 14%. The correlation coefficient between the two companies is 0.65. Find the value of E (Rp) and s (Rp). 7.88%, 15.35%

Explanation / Answer

expected return = (return of item 1 * value of item 1 + return of item 2 * value of item 2)/total value
20000/.029. The value of the stock is 70*300 cause 300 shares cost $70 each. For the treasury, it ends up being $20000. So it's present value is 20000/(1+interest rate) or 20000/1.029.

so we do (.12*70*300+.029*20000/1.029)/(70*300+20000/1.029)

now the standard deviaion generally requires we know a covariance. The formula is sqrt((weight of item 1*standard deviation of item 1)^2+2*(weight 1*weight *covariance)+(weight of item 2*standard deviation of item 2)^2

Here, the standard deviation of item 2 is 0, so the second and third term cancel out. The weight of the first term is the value of the first term/value total or 70*300/(70*300+20000/1.029).

We get

sqrt((.38*70*300/(70*300+20000/1.029))^2 which gets us the right answer.

For 2.

We use the alternative formula for portfolio standard deviation. It is sqrt((weight of item 1*standard deviation of item 1)^2+(weight of item 1*standard deviation of item 1)^2+2*weight item 1*weight of item 2*standard deviation item 1*standard deviation item 2)
the weights are gotten by doing value of item 1/value total and same for item 2.
It looks messy but it works:

.37=sqrt((25*400/(25*400+600*16)*.45)^2+(600/(25*400+600*16)*16*.35)^2+2*(x*.35*.45*600*16/(25*400+600*16)*400*25/(25*400+600*16)))

and that's your answer.

Now 3 we put it all together.
total value = 50,000 (simple addition.

So for expected return we get 29000*.12+21000*.15=6630 for actual return. For percentage we do what we did in #1, 29000/50000*.12+21000/50000*.15

for our standard deviation it's that same formula from 2.
sqrt((29000/50000*.40)^2+(21000/50000*.45)^2+2*(21000/50000*.45*.40*29000/50000*.35)))
for the actual return, just do that percent * 50000. so .346754*50000

finally 4.

total value = (200*80+34*1000)=50000
expected value = 200*80/(200*80+34*1000)*.14+34000/50000*.05=7.88%
standard deviation = sqrt((16/50*.42)^2+(34/50*.04)^2+2*(.65*.42*.04*16/50*34/50)=15.35%

Let me know if you have any questions, and please rate. Thank you.

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