Exercise_4_week7_answers
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Investment Management, Class Exercises #4Valuation, Portfolio Theory: SAA/TAA1. (i)An investor is considering buying 1,000 shares. She expects to receive a dividend of 16 pence per share in 1 year’s time and 20 pence after 2 years. She will sell the shares immediately after receiving the second dividend, at which time she expects to be paid £1.60 per share. She requires a return of 15% per annum on her investment. How much should she be willing to pay for the shares today?No. of shares = 1,000 D 1 = £0.16 D 2 = £0.20 P 2 = £1.60 r = 15% P 0 = ?⎪⎪⎭⎫⎝⎛+++++⨯=222210)1()1(1000,1r P r D r D P⎪⎪⎭⎫⎝⎛++⨯=220)15.1(60.1)15.1(20.015.116.0000,1P()1,500.191.209830.1512290.13913000,10=++⨯=P1 (ii) A company’s shares have just paid a dividend of 5 pence per share. Themarket expects dividends to grow annually at a rate of 3%, and requires a return on the shares of 7% per annum. At what price will the shares be trading?D 0 = 0.05 g = 3% p.a. r = 7% p.a. P 0 = ?gr D P -=10, where )1(01g D D +⨯=This is the formula for a growing perpetuity.1.287503.007.0)03.01(05.00=-+⨯=PNB we can only use this formula when r > g.1 (iii) As (ii), but dividends are expected to grow at 6% per annum for the next 3years (so the dividend at time 1 will be 5.3 pence) and then remain at that level in perpetuityD 0 = 0.05g 1 = 6% p.a. for 3 yearsg 2 = 0% from year 3, in perpetuity r = 7% p.a. P 0 = ?232210)1()1(1r r D r D r D P +++++=0 1 2 3P 0 D 1 D 2 D 3 Discounting2(1+r)3r23220)07.1(07.0)06.1(05.0)07.1()06.1(05.007.1)06.1(05.0++=P0.841659280.7430570.049070.0495330=++=P2. (i)A company’s earnings next year are estimated at $10 per share and to grow indefinitely at 7% p.a. Assume a risk free rate of 4%, a beta of 1.1 and an equity premium of 5%. The company expects always to payout 50% of earnings as dividend. What are the expected dividends and their growth rate? Calculate a DDM value for the company and estimate the PE for the company.EPS = $10 g = 7% r F = 4% β = 1.1 r m - r F = 5%Payout ratio = 50% E(D) = ?Growth rate of dividends = ? P 0 = ? P/E = ?Expected dividend = D 1 = E * payout ratio = $10 * 0.5 = $5If earnings per share grow by 7% and the company pays out a constant proportion as dividends, dividends will also grow at 7%.Using the CAPM to find r)(F M f i r r r R -+=β0.095)05.0(1.104.0=+=i RNow using the DDM to find P 020007.0095.0510=-=-=g r D PCalculating P/Egr E d E P -=1110/2007.0095.010/510=-=E P2. (ii) A company will pay a dividend of $5 at the end of this year. For 2 years after that the dividend wil1 grow 50% p.a. After a transition of 2 years its dividend growth will return to the rate of 6% forever. Given Rf =3%, E(RM) = 8%, beta = 2.0, calculate its DDM value.D 1 = $5g 1 = 50% for years 2 and 3 Transition of two years g 2 = 6% in perpetuityr F = 3% E(R M ) = 8% β = 2.0 P 0 = ?52552441331221110)1()1()1()1()1()1()1()1()1()1()1(r g r g D r g D r g D r g D r g D r D P trans trans +-+++++++++++++++=To calculate this we need r, and the values for the growth in the two transition periods.Using CAPM to find r)(F M f i r r r R -+=β13.0)03.008.0(203.0=-+=i RCalculating the transition period growth ratesTransition period 1 Growth rate = 0.5 - ((0.5-0.06)/3)= 0.353333Transition period 2 Growth rate = 0.353333 - ((0.5-0.06)/3)= 0.206667554320)1(19.47379)1(18.3715)1(15.225)1(11.25)1(5.7)1(5r g r r r r r r P +-++++++++++=188.3985P 150.99429.9713149.3377787.79681455.873600124.4247787600=+++++=P3 (i)A company has in issue 7% debt, redeemable at 95% in five years’ time. The debt is trading at £106 and the next interest payment is due in 1 year. What is the required return of the debt holders?Coupon rate = 7% of face value = 7% of £100 = £7 p.a. Price = £106Next coupon payment in one yearRedeemable at 95% in five years’ time r = ?55544332210)1()1()1()1()1(1r Fr C r C r C r C r C P +++++++++++=%72.4)1(95)1(7)1(7)1(7)1(717106£55432=+++++++++++=r r r r r rSolve for r using excel solver or IRR functions, your financial calculator or trial and error & linear interpolation. If you use the excel IRR function it finds a value of r that sets the cash flow equal to the price, so you have to input the price as a negative value.Final Spot Rate:554433221)1(1070)1(70)1(70)1(70)1(701000r r r r r +++++++++=55432)1(1070)0716.1(70)0605.1(70)0521.1(70)05.1(701000r +++++=1000 = 66.67 + 63.24 + 58.69 + 53.0 +1070/(1+r 5)51000 - 241.68 = 1070/(1 + r 5)5758.32 = 1070/(1 + r 5)5(1 + r 5)5 = 1070/758.32r 5 = (1.411)1/5 – 1 = 7.13%Final Forward Rate:=-=1)0716.1()0713.1(455,4f (1.411/1.3187)- 1 = 1.0699 - 1 = 7.00% Yield-to-maturity is a single discounting rate for a series of cash flows to equate these flows to a current price. It is the internal rate of return.Spot rates are the unique set of individual discounting rates for each period. They are used to discount each cash flow to equate to a current price. Spot rates are the theoretical rates for zero coupon bonds.Spot rates can be determined from a series of yields-to-maturity in an internally consistent method such that the cash flows from coupons and principal will be discounted individually to equate to the series of yield-to-maturity rates.Yield-to-maturity is not unique for any particular maturity, whereas spot rates and forward rates are unique.Forward rates are the implicit rates that link any two spot rates. They are a unique set of rates that represent the marginal interest rate in a future period. They are directly related to spot rates, and therefore yield-to-maturity. Some would argue (expectations theory) that forward rates are the market expectations of future interest rates. Regardless, forward rates represent a break-even or rate of indifference that link two spot rates. It is important to note that forward rates link spot rates, not yield-to-maturity rates.Discussion Questions4. Identify and explain the problem with mean-variance optimization when setting strategic weights. Show what other model could be used to avoid this problem.4a) Mean-variance optimization is a one-period model and does not take into account the liabilities of the investor. - SAA is a long-term process- Some institutional investors have to manage assets that are intended to meet specific liabilities (ex: DB pension plan and insurance companies)- These are liabilities that are defined in terms other than the assets of the fund When deciding the SAA, they should relate asset distribution to liabilities (in terms of expected return, risk tolerance, liquidity, time horizon).4b). Asset-liability modelling (ALM) is one solution: you can project the Cash Flows and the values of your assets and liabilities.- You first have to model/forecast your liabilities (based on demography, salary, inflation…)- Then you have to model the distribution of returns (on stocks & bonds) - Then you calculate your surplus5. “If I assume that markets are not efficient, I should actively manage my portfolio.”Carefully discuss.i. Define market efficiencyii. If markets are efficient, it’s not possible to beat (outperform) the marketiii. Explain the difference between active and passive investment strategies - If markets are efficient → passive- If fund managers are unable to beat the market → passive- If markets are not efficient, but managers are unable to beat the market →passive- If markets are not efficient AND managers are able to take advantage of the mispricing → active- So the statement is wrong because incompleteiv. Explain active strategies: trying to outperform the benchmark by finding mispriced securities/asset classes (asset allocation, portfolio rebalancing,stock selection).6. Present three different applications of the CAPM, and illustrate eachapplication using numerical examples.i. Present the CAPM: E[Rp] = Rf + β (E[Rm] –Rf)N.B.: For each application, students can draw the graph with E[Rp] and β.ii. Share selection: compare the expected return from CAPM and the expected return from valuation models.Ex: E[Rp] from CAPM = 12%, E[Rp] from fundamental analysis = 10%→ Stock overvalued by the market = unattractive → not hold or sell.iii. Market timing: rebalance your portfolio depending on market conditions - When the market goes up, you want to hold high beta stocks (β>1) to benefit from the growth → If β>1, E[Rp] > E[Rm]- When the market goes down, you want to hold low beta stocks to limit the losses → If β<1, E[Rp] < E[Rm], and if β<0, E[Rp] is positive when E[Rm] isnegative.iv. Determine the market price of risk (E[Rm] –Rf = slope of the CAPM line = reward for risk)- The size of the market risk premium reflects investors’ degree of risk aversion (how investors feel about investing in the stock market)- If the market premium is very high (=slope very steep), investors are very risk averse and nervous about investing → high E[Rp]- Ex: Rf = 3%, β=0.5 → If E[Rm] –Rf = 16%, then E[Rp]=11%- If E[Rm] –Rf = 2%, then E[Rp]=4% (for the same beta)v. Evaluating portfolio performance: compare expected return with realized return - Expected return E[Rp] = 10%- Realized return Rp = 12%- Difference = 2% = risk-adjusted abnormal return = alpha- We will talk about performance evaluation and alpha in the last lecture.7. When setting tactical weights, explain the difference between a private viewand a signal.i. A signal is a set of information used to forecast the movement of the market in thenear future = information about the broad economy- Give examples of signals in practice- Signals can be used for both equilibrium risk premium (long-term) and private view (short-term)ii. The private view is a statement about expected returns (together with a degree of confidence) = information about future excess returns- Give the equation and explain- Give an example of contrarian view.。