Mr. Hari Kumar has categorized all the available stock in the market into the following types: (i) Small cap growth stocks (ii) Small cap value…
CA Final · Advanced Financial Management · RTP · May 2025
Mr. Hari Kumar 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. Hari Kumar 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 factor are estimated to be as follows: Category of Stocks Weight in the Market Index Factor I (Beta) Factor II (Book Price) Factor III (Inflation) Small cap growth 15% 0.65 1.95 1.65 Small cap value 20% 1.25 2.23 2.15 Large cap growth 15% 2.25 3.20 8.65 Large cap value 50% 1.325 2.25 9.50 Risk Premium 8.85% -4.25% 0.80% The rate of return on treasury bonds is 5.80% Required: (a) Using Arbitrage Pricing Theory, determine the expected return on the market index. (b) Using Capital Asset Pricing Model (CAPM), determine the expected return on the market index. (c) Mr. Hari Kumar wants to construct a portfolio constituting only the 'small cap growth' and 'large cap value' stocks. If the target beta for the desired portfolio is 1, suggest what should be the composition of the same. Note: Round off calculations upto 3 decimal points.
Suggested Answer and Working Notes:
(a) Stock's return Small cap growth = 5.80 + 0.65 × 8.85 + 1.95 × (-4.25) + 1.65 × 0.80 = 4.585 Small cap value = 5.80 + 1.25 × 8.85 + 2.23 × (-4.25) + 2.15 × 0.80 = 9.105 Large cap growth = 5.80 + 2.25 × 8.85 + 3.2 × (-4.25) + 8.65 × 0.80 = 19.033 Large cap value = 5.80 + 1.325 × 8.85 + 2.25 × (-4.25) + 9.50 × 0.80 = 15.564 Expected return on market index 0.15 x 4.585 + 0.20 x 9.105 + 0.15 x 19.033 + 0.50 x 15.564 = 13.145% Alternatively, it can also be calculated as follows: - = 5.80 + [0.65 × 0.15 + 1.25 × 0.2 + 2.25 × 0.15 + 1.325 × 0.5] x 8.85 + [1.95 × 0.15 + 2.23 × 0.2 + 3.2 × 0.15 + 2.25 × 0.5] x (-4.25) + [1.65 × 0.15+2.15 × 0.2+8.65 × 0.15 + 9.5 × 0.5] x 0.8 = 5.80 + 11.925 + (-9.960) + 5.38 = 13.145% (b) Using CAPM, Small cap growth = 5.80 + 0.65 × 8.85 = 11.553% Small cap value = 5.80 + 1.25 × 8.85 = 16.863% Large cap growth = 5.80 + 2.25 × 8.85 = 25.713% Large cap value = 5.80 + 1.325 × 8.85 = 17.526% Expected return on market index = 0.15 x 11.553 + 0.20 x 16.863 + 0.15 x 25.713 + 0.50 x 17.526 = 17.726% (c) Let us assume that Mr. Hari will invest X 1 % in small cap value stock and X 2 % in large cap growth stock X 1 + X 2 = 1 0.65 X 1 + 1.325 X 2 = 1 0.65 X 1 + 1.325(1 – X 1 ) = 1 0.65 X 1 + 1.325-1.325 X 1 = 1 0.325 = 0.675 X 1 X 1 = 0.325 / 0.675 Hence, 0.481 = X 1 & X 2 = 0.519 Accordingly, 48.10% of fund should be invested in small cap growth category of stocks and balance 51.90% of funds should be invested in large cap value stocks.
Topics: Portfolio Management
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