Question

This question contains three parts. Please show your numeric answers as percentages with two decimal places (XX.XX%).

a) Assume that at the end of 2008, the level of S&P 500 index was 980, the expected annual dividend yield on the index in 2009 was 2.1%, and the expected annual growth rate in dividends in the long term was 7.5%. The long-term U.S. government yearly bond yield at the end of 2008 was 1.9%. What was the implied annual market risk premium for the U.S. stock market at the end of 2008?

b) Assume that the total returns from holding an equity portfolio were 25%, 28% and -30% in 2017, 2018 and 2019 respectively. What was the arithmetic average annual return during this three-year period? What was the geometric average annual return during this three-year period? Which average return is more suitable for making forecast of future return for this equity portfolio? Please briefly explain your choice.

c) At the end of 2019, you were a financial manager managing a growth equity portfolio for a mutual fund in New Zealand. You were valuing a stock to be added to your portfolio. You had the cash flow projection ready and had to choose a market risk premium as the input into the CAPM to estimate the cost of equity for this stock. Assume that, at the end of 2019, the implied annual market risk premium in New Zealand was 5.50% and the 90-year historical average annual market risk premium in New Zealand was 7.50%. Which market risk premium is more appropriate for this valuation exercise? Please briefly explain your choice and comment on the likely impact on valuation if you applied the unsuitable market risk premium.

Answer 1

a)

Expected Dividend in 2009 (D₁) = 2.1% of 980 = 20.58

Expected annual growth (g) = 7.5% = 0.075

Current level of S&P index = 980

Therefore, applying the Gordon formula:

P₀ = D₁ / (Discount rate – g)

980 = 20.58 / (Disc rate – 0.075)

Disc rate – 0.075 = 20.58 / 980

Disc rate – 0.075 = 0.021

Disc rate = 0.021 + 0.075

Disc rate = 0.096 = 9.60%

Therefore, annual market rate of return = 9.60%

Long term US Govt Bond yield = 1.9% (This implies the risk-free rate)

Therefore, Implied annual market risk premium = 9.60% - 1.90% = 7.70%

b)

Arithmetic average annual return = [25 + 28 + (-30)] / 3 = 7.67%

Geometric average annual return = [1.25*1.28*0.70]^1/3 = (1.12)^1/3 = 1.0385 = 3.85%

Geometric average annual return is more suitable for making forecasts of returns of any equity portfolio. This is because geometric return takes compounding into effect whereas arithmetic average does not take compounding into effect

c)

The 90 year historical average annual market risk premium should be used for the valuation exercise.

Reason – Historical average returns are a more accurate representation of the expected market returns rather than the expected market return as on just a particular date. Hence, it is a general practice that Expected Market Return be calculated using the historical market returns data while employing the CAPM model.

Likely impact if unsuitable market risk premium is used –

If 5.50% is used instead of 7.50%, then it would result in a lower expected rate of return of the stock that we are valuing. This would result in overvaluation of the stock.