Risk, Return and Portfolio Study Guide Part 6

SFM - COMPILER Question 53 May 2016 – Paper – 5 Marks The following are the data on five mutual funds: Fund Return Standard Deviation A 15 7 B 18 10 C 14 5 D 12 6 E 16 9 You are required to compute Reward to Volatility Ratio and portfolio using:  Sharpe method and  Treynor's method Assuming the risk free rate is 6%. Beta 1.25 0.75 1.40 0.98 1.50 rank these Solution Sharpe Ratio S = (R p – R f )/ σp Treynor Ratio T = (R p – R f )/ βp Where, R p = Return on Fund R f = Risk-free rate σp = Standard deviation of Fund βp = Beta of Fund Reward to Variability (Sharpe Ratio) Mutual Rp Rf Rp - RF Fund A 15 6 9 B 18 6 12 C 14 6 8 D 12 6 6 E 16 6 10 Reward to Variability (Treynor Ratio) Mutual Rp Rf Rp - RF Fund A 15 6 9 B 18 6 12 C 14 6 8 D 12 6 6 E 16 6 10 σp 7 10 5 6 9 σp 1.25 0.75 1.40 0.98 1.50 Reward to Variability 1.285 1.20 1.60 1.00 1.11 Ranking Reward to Variability 7.2 16 5.71 6.12 6.67 Ranking 2 3 1 5 4 2 1 5 4 3 SFM - COMPILER Question 54 Nov 2016 – RTP A company has a choice of investments between several different equity oriented mutual funds. The company has an amount of `1 crore to invest. The details of the mutual funds are as follows: Mutual Fund Beta A 1.6 1.0 B 0.9 C 2.0 D 0.6 E Required: If the company invests 20% of its investment in the first two mutual (i) funds and an equal amount in the mutual funds C, D and E, what is the beta of the portfolio? If the company invests 15% of its investment in C, 15% in A, 10% in E (ii) and the balance in equal amount in the other two mutual funds, what is the beta of the portfolio? If the expected return of market portfolio is 12% at a beta factor of 1.0, (iii) what will be the portfolios expected return in both the situations given above? Solution With 20% investment in each MF Portfolio Beta is the weighted average of the Betas of various securities calculated as below: (i) Investment Beta (β) Investment (Rs.Lacs) Weighted Investment A 1.6 20 32 1.0 20 20 B 0.9 20 18 C 2.0 20 40 D 0.6 20 12 E 100 122 (ii) With varied percentages of investments portfolio beta is calculated as follows: Investment Beta (β) Investment (Rs.Lacs) Weighted Investment A 1.6 15 24 30 B 1.0 30 15 C 0.9 13.5 30 D 2.0 60 10 E 0.6 6 100 133.5 Weighted Beta (β) = 1.335 (iii) Expected return of the portfolio with pattern of investment as in case i = 12% × 1.22 i.e. 14.64% Expected Return with pattern of investment as in case ii = 12% × 1.335 i.e., 16.02%. SFM - COMPILER Question 55 - Nov 2016 – RTP – Similar to - Question 25 - Nov 2011 – Paper Question 56 - Nov 2016 – RTP – Similar to - Question 28 2012 - Paper – 8 Marks May Question 57 Nov 2016 – Paper – 5 Marks The following information is available in respect of Security A: 12% Equilibrium Return 12% Market Return Rs.120 6% Treasury Bond trading at Co-variance of Market Return and Security Return 196% 0.80 Coefficient of Correlation You are required to determine the Standard Deviation of: Market Return and (i) (ii) Security Return Solution (iii) 𝐑𝐟 = 𝟔 𝟏𝟐𝟎 x 100 = 5% Applying CAPM 12% 7% β = 5% + β(12% - 5%) = β(7%) =1 β = Cov (r,m) 1 = 196 2 σm = 196 σm 2 σm 2 σm = √196 = 14 Standard Deviation of Market Return = 14 (iv) Cov (r,m) Cor. = 0.80 = Cor. = σr = 17.50% σm σr 196 14σr Standard Deviation of Security Return = 17.50% SFM - COMPILER Question 58 Nov 2016 – Paper – 5 Marks Mr. A has invested in three Mutual Fund (MF) schemes as per the details given below: Particulars MF ‘A’ MF ‘B’ MF ‘C’ Date of Investment 01-11-2015 01-02-2016 01-03-2016 Amount of Investment 1,00,000 2,00,000 2,00,000 Net Asset Value at entry date 10.30 10.00 10.10 Dividend Received upto 31-3-2016 2,850 4,500 NIL NAD as on 31-3-2016 10.25 10.15 10.00 Assume 1 year = 365 days. Show the amount of rupees upto two decimal points. You are required to find out the effective yield (upto three decimal points) on per annum basis in respect of each of the above three Mutual Fund (MF) schemes upto 31-3-2016. Solution Particulars a) Investments b) Opening NAV c) No. of Units (a/b) d) Unit NAV on 31-3-2016 e) Total NAV on 31-3-2016 (c/d) f) Increase/Decrease of NAV(a-d) g) Dividend Received h) Total Yield (f+g) i) Number of Days j) Effective yield p.a. (h/a×365/i×100) MF ‘A’ 1,00,000 10.30 9,708.74 10.25 99,514.59 (485.41) 2,850 2,364.59 152 5,678% MF ‘B’ 2,00,000 10.00 20,000 10.15 2,03,000 3,000 4,500 7,500 60 22.813% MF ‘C’ 2,00,000 10.10 19,801.98 10.00 1,98,019.86 (1980.14) NIL 1,980.20 31 (-)11.657% SFM - COMPILER Question 59 Nov 2016 – Paper – 8 Marks The returns and market portfolio for a period of four years are as under: Year % Return of Stock B % Return on Market Portfolio 1 10 8 2 12 10 3 9 9 4 3 -1 For stock B, you are required to determine: characteristic line; and (i) the Systematic and Unsystematic risk. (ii) Solution Characteristic line is given by αi +βi Rm Ʃxy−nxy βi = αi =y  − βx Ʃx2 −n(x )2 Return on B (Y) Return on B (X) 𝐗𝟐 XY 10 12 9 3 8 10 9 -1 80 120 81 -3 64 100 81 1 34 26 278 246 ) (X – 𝑿 (X –  𝐗)𝟐 (Y –  𝐘) (X –  𝐘)𝟐 1.50 3.50 2.50 1 2.25 12.25 6.25 56.25 1.50 3.50 0.50 -5.50 2.25 12.25 0.25 30.25 77.00 45.00  Y = 34/4 = 8.50  = 26/4 = 6.50 X Ʃxy−nxy β = α  = Y - βx Ʃx2 −n(x )2 = 278−4(6.50)(8.50) = 246−4(6.50)2 278−221 246−169 = 57 77 = 0.74 = 8.50 – 0.74(6.50) = 3.69 Hence the characteristic line is -3.69 + 0.74 (Rm) Total Risk of Market = σm2 = 45 4 Total Risk of Stock = Systematic Risk = β𝑖 Unsystematic Risk is Ʃ(x−x)2 n = 77 4 = 19.25% = 11.25(%) 2 σm2 = (0.74)2 × 19.25 = 10.54(%) = Total Risk – Systematic Risk = 11.25 – 10.54 = 0.71(%) SFM - COMPILER Question 60 - May 2017 – RTP – Similar to - Question 54 - Nov 2016 – RTP Question 61 May 2017 – Paper –5 Marks A is an investor and having in its portfolio shares worth Rs.1,20,00,000 at current price and cash Rs.10,00,000. The beta (β) of share portfolio is 1.4. After 4 months the price of shares dropped by 1.8%. Determine: (i) Current portfolio beta (ii) Portfolio beta after 4 months if A on current date goes for long position on Rs.1,30,00,000 Nifty futures. Show Calculations in Rs.Lakhs with four decimal points. Solution (i) Current portfolio Current Beta for share = 1.4 Beta for cash =0 Current portfolio beta = 120 130 x 1.4 + 0 x 10 130 = 1.2923 (ii) Portfolio beta after 4 months: Beta for portfolio of shares = 1.4 = Change in value of portfolio of share Change in value of market portfolio (Index) 0.018 Change in value of market portfolio (Index) Change in value of market portfolio (Index) = (0.018 / 1.4) x 100 = 1.2857 Position taken on 100 lakh Nifty futures : Long Value of index after 4 months = Rs.130 lakh x (1.00-0.012857) = Rs.128.3286 lakh Mark-to-market paid = Rs.1.6714 lakh Cash balance after payment of mark-to-market Value of portfolio after 4 months = Rs.8.3286 lakh =120 lakh×(1-0.018) +8.3286lakh = Rs.126.1686 lakh 130 lakh−126.1686 lakh Change in value of portfolio = Portfolio beta = 0.029472/0.012857 130 lakh = 2.9472% = 2.2923 SFM - COMPILER Question 62 May 2017 – Paper –8 Marks A Stock costing Rs.150 pays no dividends. The possible prices at which the stock may be sold for at the end of the year with the respective probabilities are: Price (in Rs.) Probability 130 0.2 150 0.1 160 0.1 165 0.3 175 0.1 180 0.2 Total 1.0 You are required to: calculate the Expected Return, (i) calculate the Standard Deviation ( ) of Returns. (ii) Show calculations upto three decimal points. Solution Here, the probable returns have to be calculated using the formula R= 𝐃 𝐏 𝟏 − 𝐏𝟎 + 𝐏𝟎 𝐏𝟎 Calculations of Probable Returns Possible Prices (𝐏𝟏 ) (Rs) 130 150 160 165 175 180 𝐏𝟏 - 𝐏𝟎 -20 0 10 15 25 30 [(𝐏𝟏 - 𝐏𝟎 )] x 100 Return (per cent) -13.33 0.00 6.67 10.00 16.667 20.00 Calculations of Probable Returns Possible Prices Probablility p (𝐗 𝐢 ) 𝐗 𝟏 - p(𝐗 𝐢 ) -13.33 0.00 6.667 10.00 16.667 20.00 0.2 0.1 0.1 0.3 0.1 0.2 -2.667 0.000 0.667 3.000 1.667 4.000 X = 6.667 𝐗𝐢 Product Expected return X = 6.667 per cent Alternatively, it can also be calculated as follows: Expected Price = 130 x 0.2 + 150 x 0.1 + 160 x 0.1 + 165 x 0.3 + 175 x 0.1 + 180 x 0.2 = 160 Return = 160−150 150 ×100 = 6.667% SFM - COMPILER Calculations of Standard Deviation of Returns Probable return Probablility Deviation Deviation Squared  )𝟐 (𝐗 𝐢 -𝐗) (𝐗 𝐢 -𝐗 𝐗𝐢 p (𝐗 𝐢 ) -13.33 0.00 6.667 10.00 16.667 20.00 0.2 0.1 0.1 0.3 0.1 0.2 Variance, σ = - 133.332 per cent Standard deviation, σ = √133.332 -20.00 -6.667 0 3.333 10.00 13.333 400.00 44.449 0 11.109 100.00 177.769 2 Product (𝐗 𝐢 -𝐗)𝟐 80.00 4.445 0 3.333 10.00 35.554 σ2 = 133.332 = 11.547 per cent Question 63 May 2017 – Paper –8 Marks The five portfolios of a mutual fund experienced following result during last 10 years periods : Portfolio Average annual Standard Correlation with return % Deviation the market return A 20.0 2.3 0.8869 17.0 1.8 0.6667 B 18.0 1.6 0.600 C 16.0 1.8 0.867 D 13.5 1.9 0.5437 E Market risk : 1.2 Market rate of return : 14.3% : 10.1% Risk free rate Beta may be calculated only upto two decimal. Rank the portfolio using JENSEN's ALPHA method. Solution Let portfolio standard deviation be σp Market Standard Deviation = σm Coefficient of correlation = r σp 𝑟 Portfolio beta (βp ) = σ , ( Beta for A = 2.30 x 0.8869/1.2 = 1.7, etc) m Required portfolio return (R p ) = R f + βp (R m – R f ), [R p for A = 10.1 +1.70x(14.3-10.1) = 17.24, etc.] Return from the portfolio (R p ) (%) Portfolio Beta A 1.70 17.24 1.00 14.30 B 0.80 13.46 C 1.30 15.56 D 0.86 13.71 E SFM - COMPILER Portfolio A B C D E Average Return % 20 17 18 16 13.5 Expected Return % 17.24 14.30 13.46 15.56 13.71 Question 64 Jensen’s Alpha AR – ER 2.76 2.70 4.54 0.44 -0.20 Rank II III I IV V Nov 2017 – RTP ABC Ltd. manufactures Car Air Conditioners (ACs), Window ACs and Split ACs constituting 60%, 25% and 15% of total market value. The stand-alone Standard Deviation and Coefficient of Correlation with market return of Car AC and Window AC is as follows: S.D. Coefficient of Correlation Car AC 0.30 0.6 Window AC 0.35 0.7 No data for stand-alone SD and Coefficient of Correlation of Split AC is not available. However, a company who derives its half value from Split AC and half from Window AC has a SD of 0.50 and Coefficient of correlation with market return is 0.85. Index has a return of 10% and has SD of 0.20. Further, the risk-free rate of return is 4%. You are required to determine: Beta of ABC Ltd. (i) (ii) Cost of Equity of ABC Ltd. Assuming that ABC Ltd. wants to raise debt of an amount equal to half of its Market Value then determine equity beta, if yield of debt is 5%. Solution (i) Determination of Beta of Car AC and Window AC σsm σs σm Car AC 0.6 x 0.3 0.2 = 0.90 Window AC 0.7 x 0.35 0.2 = 1.225 Beta of Split AC/ Window AC is 0.85 x 0.50 0.2 = 2.125 The Beta of Split AC alone is 2.125 = 0.50βs + 0.50βc = 0.50βs + 0.50 x 1.225 βs = 3.025 SFM - COMPILER ABC Ltd.’s Beta shall be: 0.6 x 0.9 + 0.25 x 1.225 + 0.15 x 3.025 = 1.30 (ii) Ke Cost of Equity of ABC Ltd. = 4% + 1.30(10% - 4%) = 11.80% (iii) Calculation of Debt Beta 5%−4% = 0.167 10%−4% Accordingly, Beta of Equity shall be 1.30 = 0.50 x 0.167 + 0.50 x βe = 2.433 Question 65 Nov 2017 – RTP Following is the data regarding six securities: A B C D E F Return (%) 8 8 12 4 9 8 Risk (Standard Deviation) 4 5 12 4 5 6 (i) Assuming three will have to be selected, state which ones will be picked. (ii) Assuming perfect correlation, show whether it is preferable to invest 75% in A and 25% in C or to invest 100% in E Solution Security A has a return of 8% for a risk of 4, whereas B and F have a (i) higher risk for the same return. Hence, among them A dominates. For the same degree of risk 4, security D has only a return of 4%. Hence, D is also dominated by A. Securities C and E remain in reckoning as they have a higher return though with higher degree of risk. Hence, the ones to be selected are A, C & E. (ii) The average values for A and C for a proportion of 3 : 1 will be : Risk = Return = (3×4)+(1×2) = 6% (3×8)+(1×12) = 9% 4 Therefore: Risk Return 4 75% A 25% C 6 9% E _ 5 9% For the same 9% return the risk is lower in E. Hence, E will be preferable. SFM - COMPILER Question 66 - Nov 2017 – RTP – Similar to - Question 21 - May 2011 - Paper – 5 Marks Question 67 - Nov 2017 – RTP – Similar to –Question 53 - May 2016 – Paper – 5 Marks Question 68 Nov 2017 – Paper – 10 Marks The return of security ‘L’ and security ‘K’ for the past five years are given below: Year Security – L Security – K Return % Return % 2012 10 11 2013 04 -06 2014 05 13 2015 11 08 2016 15 14 Calculate the risk and return of portfolio consisting above information. Solution If it is assumed 50% investment in each of the two securities then Return and Risk of Portfolio shall be computed as follows: Year Return Deviation Deviation Return Deviation Deviation Product of of L of K (𝐑 𝐋 - 𝐑 𝐋) (𝐑 𝐋 - 𝐑𝐋)𝟐 (𝐑 𝐊 - 𝐑 𝐊 ) (𝐑 𝐊 - 𝐑 𝐊 )𝟐 deviations 2012 2013 2014 2015 2016 10 04 05 11 15 1 -5 -4 2 6 Ʃ = 45 45  R L = 5 = 9 Covariance = 1 25 16 4 36 Ʃ = 82   ∑N i=1 [R1 −R1 ][R2 −R2 ] N = 11 -6 13 8 14 Ʃ = 40  R K = 40 =8 5 89 5 = 17.8 Return and Standard Deviation of Security L 45 RL = σL =√ L ) (RL −R σL =√ 82 =9 5 N 2 = 4.05 5 Standard Deviation of Security K σK =√ K ) (RK −R N 2 3 -14 5 0 6 9 196 25 0 36 Ʃ = 266 3 70 -20 0 36 89 SFM - COMPILER σ𝐾 =√ 266 5 = 7.26 Portfolio Return = 0.50 x 9 +0.50 x 8 Rp = 8.50% Portfolio Standard Deviation σLK = (0.502 X 4.052 + 0.502 X 7.292 + 2X 0.5 X 0.5 X 17.8)½ = 5.12 Question 69 - May 2018 – RTP – Similar to - Question 32 - May 2013 – RTP Question 70 - May 2018 – RTP – Similar to - Question 12 - Nov 2009 - Paper – 10 Marks Question 71 May 2018 – Paper – 8 Marks As an investment manager, you are given the following information: Particulars Initial Dividen Market price of the Beta (Risk Price (Rs.) d (Rs.) dividends (Rs.) Factor) A. Equity Shares: Manufacturing Ltd. 30 2 55 0.8 Pharma Ltd. 40 2 65 0.7 Auto Ltd. 50 2 140 0.5 B. Government of 1005 140 1010 0.99 India Bonds By assuming risk free return as 16%, Calculate: Expected rate of return on the portfolio (aggregate) of investor; (i) Expected rate of return of portfolio in each above stated share/ bond (ii) using Capital Asset Pricing Model (CAPM); and Average Rate of Return. (iii) Solution a) Return on market portfolio Total dividend P0 = 30+40+50+1005 D −P = ( 1P 1 ) – 1 0 = 2+2+2+140 = 146 = 1125 P1 = 55+65+140+1010 = 1270 Rm = ( 146+1270 )–1 1125 b) Average β = 0.8+0.7+0.5+0.994 4 = 25.87% = 0.7475 SFM - COMPILER i. ii. iii. Expected return on portfolio = Rf + β (Rm-Rf) = 16+0.7475(25.87-16) = 23.38% Re for each stock Manufacturing Pharma Auto GOI Average Return = = 16+0.8(25.87-16) = 16+0.7(25.87-16) = 16+0.5(25.87-16) = 16+0.99(25.87-16) 23.896+22.909+20.935+25.7714 4 = 23.896 = 22.909 = 20.935 = 25.771 = 23.378% Question 72 - May 2018 (New) – RTP – Similar to - Question 41 May 2014 – RTP Question 73 - May 2018 (New) – RTP – Similar to - Question 47 May 2015 - Paper – 8 Marks Question 74 May 2018 (New) – Paper – 10 Marks Consider the following information on two stocks, X and Y: Year 2016 2017 Return on X (%) 10 16 Return on Y (%) 12 18 You are required to determine: (i) The expected return on a portfolio containing X and Y in the proportion of 40% and 60% respectively. (ii) The Standard Deviation of return from each of the two stocks. (iii)The covariance of returns from the two stocks. (iv) Correlation coefficient between the returns of the two stocks. (v) The risk of a portfolio containing X and Y in the proportion of 40% and 60%. Solution (i) Expected return of the portfolio X and Y E (X) = (10 + 16) / 2 = 13% E (Y) = (12 + 18) / 2 = 15% Rp = 0.4 (13) + 0.6 (15) = 14.2% (ii) Standard Deviation of X and Y Stock X Variance = 0.5 (10 – 13)² + 0.5 (16– 13) ² = 9 Standard deviation = 9 = 3% SFM - COMPILER Stock Y Variance = 0.5 (12 – 15) ² + 0.5 (18– 15) ² = 9 Standard deviation = 3% (iii) Covariance of stocks X and Y COVXY = 0.5 (10– 13) (12– 15) + 0.5 (16– 13) (18– 15) = 9 (iv) Correlation of coefficient 9 Cov (X,Y) p= = 3x3=1 σx σy (v) Portfolio Risk σp= 0.4 (3) + 0.6 (3) = 3% Question 75 - Nov 2018 – RTP – Similar to - Question 22 - May 2011 - Paper - 5 Marks Question 76 - Nov 2018 – RTP – Similar to - Question 54 - Nov 2016 – RTP Question 77 Nov 2018 – RTP X Co., Ltd., invested on 1.4.2009 in certain equity shares as below: Name of Co. No. of shares Cost (Rs.) M Ltd. 1,000 (Rs.100 each) 2,00,000 N Ltd. 500 (Rs.10 each) 1,50,000 In September, 2009, 10% dividend was paid out by M Ltd. and in October, 2009, 30% dividend paid out by N Ltd. On 31.3.2010 market quotations showed a value of Rs.220 and Rs.290 per share for M Ltd. and N Ltd. respectively. On 1.4.2010, investment advisors indicate (a) that the dividends from M Ltd. and N Ltd. for the year ending 31.3.2011 are likely to be 20% and 35%, respectively and (b) that the probabilities of market quotations on 31.3.2011 are as below: Probability Factor Price/share of M Ltd. Price/share of N Ltd. 0.2 220 290 0.5 250 310 0.3 280 330 You are required to: Calculate the average return from the portfolio for the year ended (i) 31.3.2010; Calculate the expected average return from the portfolio for the year (ii) 2010-11; and (iii) Advise X Co. Ltd., of the comparative risk in the two investments by calculating the standard deviation in each case. SFM - COMPILER Solution Calculation of return on portfolio for 2009-10 (Calculation in Rs./share) M N 10 3 Dividend received during the year Capital gain/loss by 31.03.10 Market value by 31.03.10 220 Cost of investment 290 200 300 Gain/loss 20 (-)10 Yield 30 (-)7 Cost 200 300 % return 15% (-)2.33% 57 43 Weight in the portfolio 7.55% Weighted average return Calculation of estimated return for 2010-11 Expected dividend 20 3.5 33 - - 22 53 25.5 Capital gain by 31.03.11 (220x0.2) + (250x0.5) + (280x0.3) – 220 = (253-220) (290x0.2) + (310x0.5) + (330x0.3) – 290 = (312 – 290) Yield *Market Value 01.04.10 % return 220 290 24.09% 8.79% 60.3 39.7 *Weight in portfolio (1,000x220): (500x290) Weighted average (Expected) return 18.02% (*The market value on 31.03.10 is used as the base for calculating yield for 10-11) Calculation of Standard Deviation Exp. Market value 220 250 280 Exp. Gain Exp. div. Exp. Yield (1) 0 30 60 20 20 20 20 50 80 Standard Deviation (𝛔𝐌 ) M Ltd. Prob. (1) x (2) Factor (2) 0.2 0.5 0.3 4 25 24 53 Dev. 𝑃 ( P𝑚 ) M -33 -3 27 Square of Dev. (3) 1089 9 729 (2) x (3) 217.80 4.5 218.70 2 = 441 σM 21 SFM - COMPILER Exp. Market value 290 310 330 Exp. Gain Exp. div. Exp. Yield (1) 0 20 40 3.5 3.5 3.5 3.5 23.5 43.5 N Ltd. Prob. (1) x (2) Factor (2) 0.2 0.5 0.3 0.8 11.75 13.05 25.5 Dev. 𝑃 ( 𝑛) P N -22 -2 18 Square of Dev. (3) 484 4 324 Standard Deviation (𝛔𝐍 ) (2) x (3) 96.80 2.00 97.20 σ2N = 196 14 Share of company M Ltd. is more risky as the S.D. is more than company N Ltd. Question 78 Nov 2018 – Paper – 8 Marks Mr. Gupta is considering investment in the share of R. Ltd. He has the following expectations of return on the stock and the market: Probability Return (%) R Ltd. Market 0.35 30 25 0.30 25 20 0.15 40 30 0.20 20 10 You are required to: a. Calculate the expected return, variance and standard deviation for R Ltd. b. Calculate the expected return variance and standard deviation for the market. c. Find out the beta co-efficient for R Ltd. shares. Solution P R R.P. d.R. 𝐝𝟐 𝐑. 𝐏. M M.P. dm 𝐝𝟐 𝐌. 𝐏. dRdM.P 0.35 30 10.5 2 1.4 25 8.75 3.75 4.92 +2.625 0.30 25 7.5 -3 2.7 20 6 -1.25 0.47 +1.125 0.15 40 6 12 21.6 30 4.5 8.75 11.48 15.75 0.20 20 4 -8 12.8 10 2 -11.25 25.31 18 𝐗 28 𝝈𝟐 = 38.5  𝐗 21.25 𝝈𝟐 = 42.18 37.5 σ = 6.20 𝐂𝐎𝐕𝐑𝐌 = 37.5 𝛃𝐑 = 𝐂𝐎𝐕𝐑𝐌 𝛔𝟐 𝐌 = 𝟑𝟕.𝟓 𝟒𝟐.𝟏𝟖 = 0.889 σ = 6.49 SFM - COMPILER Question 79 - Nov 2018 (New) – RTP – Similar to - Question 31 Nov 2012 - Paper – 8 Marks Question 80 - Nov 2018 (New) – RTP – Similar to - Question 53 May 2016 – Paper – 5 Marks Question 81 Nov 2018 (New) – Paper – 8 Marks Mr. Kapoor owns a portfolio with the following characteristics: Security X Security Y Risk Free Security Factor 1 Sensitivity 0.75 1.50 0 Factor 2 Sensitivity 0.60 1.10 0 Expected Return 15% 20% 10% It is assumed that security returns are generated by a two factor model. a. If Mr. Kapoor has Rs.1,00,000 to invest and sells short Rs.50,000 of security Y and purchases Rs.1,50,000 of security X, what is the sensitivity of Mr. Kapoor's portfolio to the two factors ? b. If Mr. Kapoor borrows Rs.1,00,000 at the risk free rate and invests the amount he borrows along with the original amount of Rs.1,00,000 in security X and Y in the same proportion as described in part (i), what is the sensitivity of the portfolio to the two factors ? c. What is the expected return premium of factor 2? Solution Mr. X’s position in the two securities are +1.50 in security A and - 0.5 i. in security B. Hence the portfolio sensitivities to the two factors:b prop. 1 =1.50 x 0.75 + (-0.50 x 1.50) = 0.375 b prop. 2 = 1.50 x 0.60 + (-0.50 x 1.10) = 0.35 ii. Mr. X’s current position:Security A Rs.3,00,000 /Rs.1,00,000 =3 Security B –Rs.1,00,000 /Rs.1,00,000 = -1 Risk free asset –Rs.100000 /Rs.100000 = -1 b prop. 1 = 3.0 x 0.75 + (-1 x 1.50) + (- 1 x 0) = 0.75 b prop. 2 = 3.0 x 0.60 + (-1 x 1.10) + (-1 x 0) = 0.70 iii. Expected Return = Risk Free Rate of Return + Risk Premium Let λ1 and λ2 are the Value Factor 1 and Factor 2 respectively. Accordingly 15 = 10 + 0.75 λ1 + 0.60 λ2 20 = 10 + 1.50 λ1 + 1.10 λ2 On solving equation, the value of λ2 = 0, the expected return premium of factor 2 = 0.