Question

1. The following macroeconomic projected return models

π = inflation and GDP = GDP growth

RBAH=9.2+0.2Fπ+ 0.8FGDP+ϵ

RFIVN=11.6-0.6Fπ+ 1.8 FGDP+ϵ

RSP500=8.8-1.2 Fπ+ 1.6 FGDP+ϵ

1. Expected inflation is 2.3% and actual inflation may be greater by 0.4%, calculate the impact on the S&P500 projected return ( How would the projected return change)
2. Create a portfolio invested in Boaz Allan (BAH) and Five9 (FIVN) with the same exposure to GDP as the S&P500.
3. Create a portfolio invested in Boaz Allan (BAH) and Five9 (FIVN) to diversify away exposure to inflation.

2.

1. Given the following information

	E(R )	S
BAH	8%	10%
FIVN	14%	16%
SSNC	11%	11.78%

             Corr (Bah,FIVN) = 0.4

Does an arbitrage opportunity exist?

Answer 1

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Answer:

2.

Lets consider a portfolio of 50% BAH and 50% FIVN

Then the expected return on the portfolio is

0.5*0.08 + 0.5*0.14 = 0.11 = 11%

This expected return is the same as the return on SSNC

The standard deviation of portfolio =

where x and y are the securities

Now, the standard deviation of the portfolio = ((0.5*0.1)^2 + (0.5*0.16)^2 + 2*0.5*0.5*0.1*0.16*0.4)^0.5

The standard deviation of the portfolio = 0.11 = 11%

Now, since the returns of the portfolio and SSNC are the same, they should have the same standard deviation, otherize an arbitrage opportunity exists.

Here SSNC has a higher standard deviation than the portfolio and hence an arbitrage opportunity exist as SSNC is riskier than the portfolio while having the same expected return. An arbitrageur would buy the portfolio, and short the SSNC stock and invest the proceeds at a risk-free rate, ebentually, closing the short position by selling the portfolio, thus pocketing a risk-free profit.