Mr. NK has categorized all the available stock in the market into the following types: (i) Small cap growth stocks (ii) Small cap value stocks (iii)…
CA Final · Advanced Financial Management · RTP · January 2026
Mr. NK has categorized all the available stock in the market into the following types: (i) Small cap growth stocks (ii) Small cap value stocks (iii) Large cap growth stocks (iv) Large cap value stocks Mr. NK also estimated the weights of the above categories of stocks in the market index. Further, the sensitivity of returns on these categories of stocks to the three important factors are estimated to be: Category of Stocks Weight in the Market Index Factor I (Beta) Factor II (Book Price) Factor III (Inflation) Small cap growth 25% 0.80 1.39 1.35 Small cap value 10% 0.90 0.75 1.25 Large cap growth 50% 1.165 2.75 8.65 Large cap value 15% 0.85 2.05 6.75 Risk Premium 6.85% -3.5% 0.65% The rate of return on Treasury Bonds is 4.50%. Required: (i) Using Arbitrage Pricing Theory, determine the expected return on the market index. (ii) Using Capital Asset Pricing Model (CAPM), determine the expected return on the market index. (iii) Mr. NK wants to construct a portfolio constituting only the 'Small cap value' and 'Large cap growth' stocks. If the target beta for the desired portfolio is 1, suggest the composition of his portfolio.
Suggested Answer and Working Notes:
(i) Method I Stock's return Small cap growth = 4.5 + 0.80 x 6.85 + 1.39 x (-3.5) + 1.35 x 0.65 = 5.9925% Small cap value = 4.5 + 0.90 x 6.85 + 0.75 x (-3.5) + 1.25 x 0.65 = 8.8525% Large cap growth = 4.5 + 1.165 x 6.85 + 2.75 x (-3.5) + 8.65 x 0.65 = 8.478% Large cap value = 4.5 + 0.85 x 6.85 + 2.05 x (-3.5) + 6.75 x 0.65 = 7.535% Expected return on market index 0.25 x 5.9925 + 0.10 x 8.8525 + 0.50 x 8.478 + 0.15 x 7.535 = 7.7526% Method II Expected return on the market index = 4.5% + [0.1 x 0.9 + 0.25 x 0.8 + 0.15 x 0.85 + 0.50 x 1.165] x 6.85 + [(0.75 x 0.10 + 1.39 x 0.25 + 2.05 x 0.15 + 2.75 x 0.5)] x (-3.5) + [(1.25 x 0.10 + 1.35 x 0.25 + 6.75 x 0.15 + 8.65 x 0.50)] x 0.65 = 4.50 + 6.85 + (-7.3675) + 3.77 = 7.7525%. (ii) Using CAPM, Small cap growth = 4.5 + 6.85 x 0.80 = 9.98% Small cap value = 4.5 + 6.85 x 0.90 = 10.665% Large cap growth = 4.5 + 6.85 x 1.165 = 12.48% Large cap value = 4.5 + 6.85 x 0.85 = 10.3225% Expected return on market index = 0.25 x 9.98 + 0.10 x 10.665 + 0.50 x 12.45 + 0.15 x 10.3225 = 11.33% (iii) Let us assume that Mr. NK will invest X 1 % in Small cap value stock and X 2 % in Large cap growth stock X 1 + X 2 = 1 0.90 X 1 + 1.165 X 2 = 1 0.90 X 1 + 1.165(1 – X 1 ) = 1 0.90 X 1 + 1.165 – 1.165 X 1 = 1 0.165 = 0.265 X 1 X 1 = 0.165 / 0.265 0.623 = X 1 and X 2 = 0.377 62.30% in Small cap value stocks 37.70% in Large cap growth stocks.
Topics: Portfolio Management
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