Question

You are asked to analyze Portfolio X. You collect the following data: a. Assuming a risk-free rate of 4%, what is the expected return of Portfolio X according to Arbitrage Pricing Theory (APT) [note: you may assume the only two relevant factors are "Quality" and the market for the purposes of this calculation]? b.Your research department is convinced the actual forward-looking return for Portfolio X is 11%. Using that expectation combined with your answer in part a, construct a profitable arbtrage that combines Portfolio X with (i) the Quality Factor ETF, (ii) the Market Portfolio, and (iii) Treasury Bills.

Answer 1

To calculate the expected return of Portfolio X according to Arbitrage Pricing Theory (APT), assign weights to the relevant factors and calculate the weighted average. To construct a profitable arbitrage, combine Portfolio X with the Quality Factor ETF, the Market Portfolio, and short Treasury Bills.

Step-by-step explanation:

To calculate the expected return of Portfolio X according to Arbitrage Pricing Theory (APT), we need to consider the relevant factors, which in this case are 'Quality' and the market. Assuming a risk-free rate of 4%, you would assign a weight to each factor based on their expected returns and the sensitivity of Portfolio X to each factor. For example, if the expected return on Quality is 10% and it has a weight of 0.5, and the expected return on the market is 8% with a weight of 0.5, the expected return of Portfolio X would be (10% * 0.5) + (8% * 0.5) = 9%.

Now, if your research department believes that the forward-looking return for Portfolio X is 11%, you can use this expectation along with your answer in part a to construct a profitable arbitrage. Arbitrage involves taking advantage of price differences between securities in different markets. To construct the arbitrage, you can take a long position in Portfolio X, buy the Quality Factor ETF and the Market Portfolio, and short Treasury Bills.