Investment and Portfolio Management

Question 1
(a). Today is 1 January. You have received 10,000 equity shares of a listed company under a share compensation plan. These shares are currently selling at $30 each. You plan to buy a new home in July and therefore, you want to defer selling these shares till 30 June. However, you are concerned about the risk that you won’t be able to have sufficient money for the down payment for the new home if the share prices have gone down substantially. You consider using option strategies to minimise the risk of making losses from selling your shares in June. The data related to options are given below:

Call options
Exercise price on 30 June $35 Current call premium $1

Put options
Exercise price on 30 June $25
Current put premium $2

(i). List three option strategies you can use to minimise losses from selling your shares in June. Perform necessary calculations to evaluate each strategy with respect to your investment goals.

(ii). Which strategy would you choose? Use the calculations you perform above to justify your choice.

(iii). List one advantage and disadvantage of each strategy
Marks 7+4+3 =14

(b). The multiplier for a futures contract on the S&P/ASX 200 index is $100. The maturity of the contract is one year, the current level of the index is 4550 and the risk-free rate is 0.60% per month. The dividend yield on the index is 0.30% per month. Suppose that after two months the stock index is 4660.

(i). Find the cash flow from the mark-to-market proceeds on the contract assuming that the parity condition always holds exactly.

(ii). Find the two-month holding-period return if the initial margin is $25,000.

Marks 2+2 =4
Total marks = 18

Question 2
(a). Differentiate between an open-end fund and a close-end fund.

(b). Briefly describe an exchange traded fund and a real estate investment trust.

(c). Gamma company paid a dividend of $0.80 per share last year. Gamma company’s retention ratio for the next two years and return on equity are 50% and 30%, respectively. From the third year, Gamma company will increase its dividend payout ratio to 60%. Gamma company expects to maintain its dividend payout ratio at this level till perpetuity. If Gamma company’s investors require a rate of return of 20%, what are Gamma company’s current share price and present value of growth opportunities?

(d). Standard deviation of the market index is 15.4%. Standard deviation of a managed portfolio is 22.0%. Risk-free rate of return is 5%. The market index has a return of 12% and the managed portfolio has a return of 18.0%. From the above information, calculate M2 measure and interpret its value.

(e). Consider the following information regarding the performance of a money manager in March 2018. The table presents the actual return of each sector of the manager’s portfolio in the fraction of portfolio allocated to each sector, the benchmark sector allocations and the returns of the sector indices.

 Actual return (%)   Actual weight   Benchmark weight    Index return (%) 

Equity 2.50 0.40 0.50 3.00
Bonds 2.00 0.50 0.40 1.80
Cash 0.60 0.10 0.10 0.70

Using the above information, perform calculations to answer the following questions:

 (i). Has the manager under- or over-performed? 

(ii). Determine the contribution of security selection and asset allocation to relative performance.

(iii). Confirm that the sum of security selection and asset allocation equal manager’s total excess return relative to benchmark.

Marks 4+2+4+2+5 = 17 marks

Question 3
(a). Briefly explain the shortcoming of covariance as a measure of the relationship between the returns on two financial assets.
(b). Using your own figures explain how to achieve a zero standard deviation for a portfolio of two shares which are perfectly negatively correlated.
(c). The following are data for two shares, X and Y:
Share X Share Y
Return 0.20 .15
Standard deviation 0.08 .10

If the correlation coefficient between share X and Y is -0.20 determine the weights for shares X and Y in order to minimise the variance of the portfolio.
(d). Form a portfolio using the weights you calculated in part c above and calculate the return and risk of this portfolio.
(e). What is capital market line? What does its slope indicate?
1+2+2+6+2 = 13 Marks

Question 4

(a). Briefly explain the three stages of the investment management process.

(b). Differentiate between strategic asset allocation and tactical asset allocation.

(c). You have been the financial advisor of Mrs Judy Wu, age 65, for ten years since the death of her husband, Dr Simon Wu. Dr Wu had built a successful business that he sold four years before his death to Gamma Enterprises in exchange for Gamma’s ordinary shares. The Wus have no Children and their wills provide that upon their deaths the remaining assets shall be used to create a fund for the benefit of a hospital, to be called the Wu Endowment Fund.

The hospital is a 240-bed, not-for-profit hospital with an annual operating budget of $17 million. In the past, the hospital’s operating revenues have often been sufficient to meet operating expenses and occasionally even generate a small surplus. In recent years, however, rising costs and declining occupancy rates have caused hospital to run a deficit. The operating deficit has averaged $400,000 to $560,000 annually over the last several years. Existing endowment assets (i.e. excluding the Wu’s estate) of $10 million currently generate approximately $500,000 of annual income, up from less than $300,000 five years ago. This increased income has been the result of somewhat higher interest rates, as well as a shift in asset mix toward more bonds. To offset operating deficits, the Board of Governors of the hospital has determined that the endowment’s current income should be increased to approximately 7% of total assets (up from 5% currently). The hospital has not received any significant additions to its endowment assets in the past five years. Mrs Wu seeks your advice in respect of the following for the Wu Endowment Fund to be created after her death.

(i). Identify and describe an appropriate set of investment objectives

(ii). Describes the constraints that the Wu Endowment Fund might face

Marks 6+4+10 =20

Question 5
(a). Differentiate between a dealer market and an auction market. Give an example for each.

(b). Briefly explain the meanings of market order, stop sell order, and stop buy order using your own figures.

(c). What is a margin call?

(d). How do margin trades magnify both the upside potential and downside risk of an investment portfolio? Explain using your own figures.

(e). What is a short sale in equity shares? Explain how a short sale is conducted.

(f). Current selling price of a stock is $70. You want to sell 300 shares of this stock. You don’t own this stock at present. The initial margin requirement is 50%. Using the above information, answer the following questions:

(i). What is your equity?

(ii). If the maintenance margin is 25%, how much can you withdraw from your margin account?

(iii). Determine the price at which you would get a margin call.

(iv). If you get a margin call, how much would you have to deposit in order to restore the initial margin?

2+3+1+3+2+7 = 18 marks

Question 6

(a). Beta company’s share price and dividend history are as follows:

Year End-of-year price Dividend paid at year-end
2014 $200 $4
2015 $220 $4.5
2016 $180 $3.5
2017 $190 $4

Share price at the beginning of 2014 was $190. An investor buys four shares at the beginning of 2014, buys another two shares at the end of 2014, sells two shares at the end of 2015, buys another two shares at the end of 2016, and sells all remaining shares at the end of 2017.

(i). What is the geometric average rate of return for the investor?

 (ii). What is the dollar-weighted rate of return?  

Marks 3+5 = 8

(b). The a company’s cash flow from operations before interest and taxes was $4 million in the year just ended and it expects that this will grow by 6% per annum for ever. To make this happen, the firm will have to invest an amount equal to 25% of pre-tax cash flow each year. The tax rate is 30%. Depreciation was $400,000 in the year just ended and is expected to grow at the same rate as the operating cash flow. The appropriate market capitalisation rate for the unlevered cash flow is 15% per annum and the firm currently has debt of $8 million outstanding. Use free cash flow approach to value the firm’s equity.

Marks 6
Total Marks=14

BAO 3403 Investment and Portfolio Management
Formula Sheet
1.Price of bond futures contracts (P)

1− 𝑣𝑣𝑛𝑛 𝑛𝑛) 

𝑃𝑃 =1000× 𝑐𝑐 × +(100× 𝑣𝑣
® = yield to maturity/200, v = 1/(1+ i) n = 20, c = coupon/2 = 3 2. Holding period return (HPR) HPR = [PS – PB + CF] / PB
PS = Sale price, PB = purchase price
CF = Dividend/Cash flow during holding period

  1. Arithmetic Average HPRavg

n = number of time periods, HPRT = HPR for period T 4. Geometric average HPRavg

n = number of time periods

  1. Beta of security ® (βi)

βi = σM2i ,rM )
COV(r ,r ) = covariance between the return of
i M security € and market return σM = standard deviation of the market return

Note: Alternatively, if the change in the returns for a particular change in the market return is given, we can roughly estimate the beta by dividing the change in the share reruns by the change in the market return.
6. Beta of a portfolio(βp)

βp = Wiβi

Wi = weight for security ® βi = beta of security i

  1. Expected return of a two-security portfolio

E(rp) = W1E(r1)+ W2E(r2)

W1 = Proportion of funds in security 1 W2 = Proportion of funds in security 2 E(r1) = Expected return on security 1 E(r2) = Expected return on security 2
8. Variance of a two security portfolio (σP2 )
σP = (W1σ1)2 + (W2σ2)2 + 2W1W2Cov(r1,r2)

W1 = Proportion of funds in security 1 W2 = Proportion of funds in security 2
Cov(r r ) = covariance between returns of security 1 and
1 2
σ1 = standard deviation of returns of security 1 σ2 = standard deviation of returns of security 2

  1. Capital Asset Pricing Model (CAPM)

ri= rf + βi(rM – rf) ri = return on security i rf = risk-free rate of return βi = beta of security i rM = expected market return 10. Dollar Weighted Return (DW
CF0 = CF1 1 + (1+CFDWR2 )2 +… + (1+CFDWRn )n
CF = net cash flow

Note: The subscripts and superscripts are period numbers.

  1. Covariance between two securities – ex post returns
    n (r1,T − r 1 )×(r2,T − r 2 )
    Cov(r1,r2) =∑ n -1
    Cov (r1,r2) = covariance between returns of security
    1 and 2
    n = number of observations, T = time r1,T = return of security 1 at time T r2,T = return of security 2 at time T ̅r1 = average return of security 1 r̅ 2 = average return of security 2 12. Correlation between two securities
    Cov(r ,r2) 1 2 ρ(1,2) = correlation between returns of security 1 and 2 Cov (r1,r2) = covariance between returns of security 1 and 2
    σ1 = standard deviation of returns of security 1 σ2 = standard deviation of returns of security 2
  2. Expected return of a security – ex ante
    E(r) =∑psrs
    E® = expected return of security
    Ps = probability for economic condition i rs=return of the security in economic condition i 14. Present value of a share ((V0) when dividends grow at a constant rate
    V0 = kD−1g
    K= market capitalisation rate/required rate of return g=constant growth rate of dividends
    Note: In equilibrium V0 =P0 (current market price)
  3. Present value of growth opportunities
    PVGO = D1 − E1 k −g k
    E1 = earnings at the end of period 1 16. Present value of a share when there are two growth periods

D0 = current dividend
g1=growth of dividends during the first growth period g2 = growth of dividends during the first growth period T= duration of the first growth period
t= period number, D0 = dividend just paid by the company
Note: In equilibrium V0 =P0 (current market price)

  1. Value of a firm according to free-cash flow method (FCFF)

WACC = Weighted average cost of capital g = estimate of long run growth in free cash flow
T = time period when the firm approaches constant growth
PT = terminal value of the firm

Note: Value of an equity share = (firm value – debt)/number of shares outstanding 18. Duration of a bond (Macaulay duration)(D)

D = duration

Wt = Weight of time t, present value of the cash flow earned in time t as a per cent of the amount invested
CFt = Cash flow in time t, coupon in all periods except terminal period when it is the sum of the coupon and the principal ytm = yield to maturity

  1. Modified duration of a bond (D) D = D/ (1+ytm)
    1. Spot-futures parity
      F0 = S0(1+rf-d)T
      S0 = spot price at time 0, F0 = futures price at time T rf = risk-free rate of return, d = dividend yield
      Note: if the asset does not pay dividends, d in the above equation is 0.
  2. Break-even point for a call option
    S = X + C
    T 0
    ST = value of asset at time T
    X = exercise price
    C0 = call premium
  3. Sharpe measure/ratio (S)
    S= rp −rf
    rp = return of the portfolio, rf = risk-free rate of return
    σp = standard deviation of the portfolio return
  4. Sharpe’s ratio (S) of the optimised risky portfolio
    S2 =SM2 +A2 A = α/σ®
    α = alpha of the risky portfolio
    σ®= residual variance of the risky portfolio SM = Sharpe measure of the active portfolio
    1. Alpha of asset ® (αi) αi = ri – [rf + βi(rM – rf )]
      Note: see equation 9 for the definitions of variables
  5. Modigliani-squared’ (M2) measure

M2 = E(rP) – E(rM) E(rP)= expected return of the risky portfolio E(rM) = expected return of the passive portfolio

  1. Weight for asset i (Wi) in the risky portfolio

αi = alpha of a asset i
σ2i(e)= residual variance of an asset i

  1. Expected alpha (α) of the risky portfolio
    Note: Wi is calculated using equation 26 28. Expected alpha (β) of the risky portfolio
    βP =∑βiWi
    Note: Wi is calculated using equation 26
  2. Expected residual variance (σ2(e) ) of the risky portfolio
    σ (e) =∑Wi2σi2
    Note: Wi is calculated using equation 26 30. Weight of the risky portfolio (w) w= w0

w0 = α/σ2(e) 2
[E(rM ) −rf ]/σM

  1. Leading PE ratio=P0/E1

P0= current share price
E1= earnings per share in period 1 32. Trailing PE ratio=P0/E0

E0 = current earnings per share

  1. Total risk of security ® (σi2 ) σi =systematic risk + unsystematic risk 2 2 2 2 2 σi =βi σM +σ (ei ) βi = beta of security i σM = standard deviation of market return σ2€ = standard deviation of the error term
    1. Capital allocation line (CAL)
      E(rP ) = rf + M −rf σP r
      E(rp) = expected return of a portfolio
  2. Variance of share returns (σ2) – ex ante σ2 =∑p(s)×[rs − E(r)]2 s P(s) = probability of state s rs = return in state s E(r) = expected return (see equation 13)
    1. Choosing the weights to minimise variance of a portfolio
      W , W2 = 1-W1
      W1 = proportion invested in security 1 W2 = proportion invested in security 2
      Note: other symbols are as defined earlier
  3. Break-even point of a put option

ST = X –P0
X = exercise price
P0 = put premium