If the correlation between Pluto and Neptune is 0.25, determine the expected return and standard deviation of a portfolio that consists of 65% Pluto Corporation stock and 35% Neptune Corporation stock.

**A)**

10.3% expected return and 2.58% standard deviation.

**B)**

10.3% expected return and 16.05% standard deviation.

**C)**

10.0% expected return and 16.05% standard deviation.

**Your answer: B was correct!**

ER_{Port}

= (W_{Pluto})(ER_{Pluto}) + (W_{Neptune})(ER_{Neptune})

= (0.65)(0.11) + (0.35)(0.09) = 10.3%

σ_{p}

= [(w_{1})^{2}(σ_{1})^{2} + (w_{2})^{2}(σ_{2})^{2} + 2w_{1}w_{2}σ_{1}σ_{2} r_{1,2}]^{1/2}

= [(0.65)^{2}(22)^{2} + (0.35)^{2}(13)^{2} + 2(0.65)(0.35)(22)(13)(0.25)]^{1/2}

= [(0.4225)(484) + (0.1225)(169) + 2(0.65)(0.35)(22)(13)(0.25)]^{1/2}

= (257.725)^{1/2} = 16.0538%

**Why use 13 and 22 instead of .13 and .22??**

*ALSO*

Current spot rates are as follows:

1-Year: 6.5% 2-Year: 7.0% 3-Year: 9.2%

Which of the following is CORRECT

A)

For a 3-year annual pay coupon bond, all cash flows can be discounted at 9.2% to find the bond’s arbitrage-free value.

B)

For a 3-year annual pay coupon bond, the first coupon can be discounted at 6.5%, the second coupon can be discounted at 7.0%, and the third coupon plus maturity value can be discounted at 9.2% to find the bond’s arbitrage-free value.

C)

The yield to maturity for 3-year annual pay coupon bond can be found by taking the geometric average of the 3 spot rates.

Your answer: C was incorrect. The correct answer was B) For a 3-year annual pay coupon bond, the first coupon can be discounted at 6.5%, the second coupon can be discounted at 7.0%, and the third coupon plus maturity value can be discounted at 9.2% to find the bond’s arbitrage-free value.

Spot interest rates can be used to price coupon bonds by taking each individual cash flow and discounting it at the appropriate spot rate for that year뭩 payment. Note that the yield to maturity is the bond뭩 internal rate of return that equates all cash flows to the bond뭩 price. Current spot rates have nothing to do with the bond뭩 yield to maturity

*Should be 6.5 for first year then 7^2 for second year and 9.2^3 for third year. Right….???*