You determine that there are two factors under the APT that affect the portfolios you have constructed for your limited clientele, who invest only in gold equities: the rate of inflation and the growth rate of all gold stocks in relation to the growth rate of all commodity equities. You determine that the two factors will grow by 0.08 and 0.20, respectively, with zero covariance between the two factors, and the zero beta portfolio’s expected rate of return is 3 per cent. The beta for your gold portfolio is 1.2 with respect to both factors.

Calculate the expected rate of return for your portfolio. (25 marks)

Assume a two-factor APT model is appropriate for asset returns, and there are an infinite number of assets in the economy. Two factors drive expected return: the percentage change in GDP and interest rates. The crosssectional relationship between expected return and factor betas indicates that GDP is expected to grow by 5 per cent and interest rates will grow by 2 per cent. You have estimated factor betas for equities X and Y as follows:
Equity β1 β2 X 2.3 1.9 Y 0.6 −0.5