Question

An investor holds shares of Bank of Montreal. The Canadian stock market can be explained by three sources of systematic risk: short-term interest rates (I), the rate of inflation (P), and industrial production (Y). Short-term interest rates have an associated risk premium of 4%, inflation has an associated risk premium of 4% and industrial production has an associated risk premium of 1%. Each systematic factor has a mean value of zero, so that non-zero factor values represent unexpected surprises from prior expectations.   The excess return for the stock can be described by the following formula:
R = 0.11 + 0.8 I + 0.3 P + 1.1 Y + e

What is the stock's alpha according to the APT? Enter your answer as a decimal number or with the percentage sign.

Answer 1

Arbitrage price theorem explains that under normal conditions any investor will not be able to earn excess returns over the long period of time.

It can be explained as, excess return earned based on selection of risk factors and its volatility.

Formula = E(R) = Risk free rate + risk factor sensitivity 1 * Risk premium 1 + risk factor sensitivity 2 * Risk premium 2...

As per the given equation, Excess return of stock is,

R= 0.11 + 0.8I + 0.3P+1.1Y+e

To understand the excess return we need to add the risk premium associated with each risk factor in given equation,

R = 0.11 + 0.8(4%)+0.3(4%)+1.1(1%)+e

R = 0.11+0.032+0.012+0.011+e

R = 0.165