1 ACST404/771/871 ASSIGNMENT 1 2016: Due Date 21 September 2016 Question 1 25 marks A university endowment fund has sought your advice on its fixed-income portfolio strategy. The characteristics of the portfolio's current holdings are listed below. These bonds (except the ZCBs) generate coupon interest income once a year. bond Maturity (years) Credit Spread % Coupon Rate % MD Convexity Yield (%) Price per 100 Face Value A 3 0.00 0% 2.899 11.2 3.50 90.19 B 10 0.40 8% 6.803 61.9 7.40 104.14 C 5 0.60 12% 3.96 21.13 5.10 129.79 D 7 0.20 10% 5.239 36.32 5.70 124.26 E 12 0.80 0% 11.029 131.79 8.80 36.35 The endowment fund is set up to provide scholarships for students at the start of the year for this year and the subsequent 14 years. The fund provides $1m in scholarships this year and the amount grows at g=4% in each subsequent year. The university uses a yield of i = 8% p.a. to estimate the amount of money to be invested in the endowment fund. You estimate the value to be $11.7m and the valuation was done 2 days before the first payment from the endowment fund is made. You computed the modified duration of the endowment fund's liabilities and found it to be 5.83 years to 2 decimal places You were advised to use the formula ൌܦܯ 1 ݎ ቀ1 ൅ ݅ 1 ቁ ቊ1 ൅ ቆ1 െ ሺ1 ൅ ݎ ݎሻିሺ௡ିଶሻቇ െ ሺ݊ െ 1ሻሺ1 ൅ ݎሻିሺ௡ିଵሻቋ 1 ൅ ൬1 െ ሺ1 ൅ ݎ ݎሻିሺ௡ିଵሻ൰ where ൌݎ ݅ െ ݃ 1 ൅ ݃ , ݊ ൌ 15 The bond portfolio is equally weighted so each of the above bonds is 20% of the fund's market value (a) Check whether the above formula for the modified duration of the liabilities is correct. Show working 4 marks2 (b) Calculate the modified duration of the equally weighted bond portfolio. Does the MD of assets equal the MD of the liabilities? Suppose there is an upward parallel shift in the yield curve of 10 basis points. What is the impact on the net position of the fund in this scenario? 4 marks (c) What is the effect on the MD of the liabilities of making the first payment of $1m from the fund? Will the MD go up or go down? By how much? Assume we liquidate part of our bond holdings to make the payment and that afterwards the bond portfolio is still equally weighted. 4 marks (d) How would this change to the liabilities (making the first payment) change the impact of a 10 basis point increase / parallel shift in yields on the net position of the fund? 4 marks (e) What combination of bonds A and B would protect the fund against parallel shifts in the yield curve in the scenario in (c)? 2 marks (f) Your current active view for the fixed income market is that treasury yields will decline and corporate credit spreads will also decrease. How might you restructure the bond portfolio to take advantage of this view? 4 marks (g) Why is a duration matching strategy more practical than a cashflow matching (dedication) strategy for management of interest rate risk? 3 marks Question 2 25 marks (a) You have been asked to calculate the value of growth opportunities for a stock but have only been given the following information. You were informed that this year, the stock's return on equity matched the market's capitalisation rate. Can you calculate this from the information provided below and if not, what additional information do you require? (15 Marks) Sales for the year $5,000,000 Depreciation for year $ 150,000 Interest paid $ 75,000 Risk Free Rate 2.00% Company Beta 1.20 Total Asset Turnover 2.00 Return on Assets 0.25 Gearing (Assets/Equity) 2.50 Company Tax Rate 30.0% Plowback ratio 70.0%3 (b) What was the stock's performance against its market capitalisation rate? What does this assume about book and market values of equity? If market value of equity was higher or lower than book value, how would this affect performance? How (5 Marks) (c) Consider the Dividend Discount Model and discuss the relationship between growth, return on equity and valuation paying attention to risk. (5 Marks) Question 3: Derivatives (25 marks) A very risk averse, very rich relative has $1m to invest and is constantly complaining to you about the fact that they can only get a fixed term deposit rate of 4.0% at the bank. You are surfing the ASX/SFE web site one day, and notice that the one year BHP futures contract is trading at $22.00 (this is the delivery price for a 1 year futures contract). The current BHP stock price is $20. The BHP futures contract has 1000 BHP shares as the underlying asset. Due to poor operating results, no dividends are payable by BHP for the next year. Assume that the futures contract requires no up front initial deposit and that there are no variation margin payments to worry about, so that the futures is really a forward contract. Using this information we want to construct a set of transactions using shares, futures and your relative's $1m in cash, so that the relative receives a riskless fixed rate of interest of 5.6% for one year, and you receive a small profit up front of $40,000 for arranging the transaction. (i) Show that if you buy 1000 shares and short 1 futures contract and hold your position for 1 year then the initial cost is $20,000 and after 1 year your payoff is $22,000. 5 marks (ii) Show that if you create a multiple of 48 times this combination of shares and futures over it will provide a payoff of $1,056,000 in 1 year's time and will have an initial cost of $960,000 so this would provide you with the arranger's fee of $40,000 2 marks (iii) How would the requirement for an initial deposit for the futures contracts and the possibility of having to pay variation margins on the futures impact on the viability of this strategy? What effect if any would the volatility of the shares have on this? 5 marks (iv) The function C S y X r T Se N d Xe N d   , , , , ,     yT rT  1 2    is the value of a European call option. Suppose   0 is some constant. Using the concept of arbitrage, show that C S y X r T C S y X r T      , , , , , , , , , ,       . Hint: consider the payoff at maturity and try α = 2 for example. 3 marks4 (v) A funds management company sells a capital guaranteed, equity linked bond to retail investors. The bond:  has a face value of $100.00 and  has a price of $100.00 as well.  has a term of 2 years and  pays no interest until maturity.  At maturity the bond will pay the face value plus a guaranteed return of K of the face value plus a proportion α of the return on the share price index in excess of K. The payoff at maturity on the bond is : payoff K S S K       100 1 max 100 100 1 ,0      T 0     Where  St is the stock market price index at time t, and T is the maturity date of the bond.  K is the guaranteed minimum return on the insurance company bond  α is the "participation rate", i.e. the proportion of the (excess) return on the stock market price index The risk free interest rate is r=6% p.a. continuously compounded. The volatility of the stock price index is σ = 30%. The dividend yield on the portfolio of stocks making up the index is y=4%. The insurance company is offering a participation rate of α = 50% when K = 10.25%. Question: Is this participation rate α = 50% fair to the customer when K = 10.25%?is the guaranteed return on the bond over the 2 year term? Use the black scholes formula to determine whether or not this is a fair price for the capital guaranteed equity linked bond. Show full details of your working. Hint: what is the time 0 value of the payoff and how does this compare to the price paid for it by the customer? The ratio V S S V S S V S S t t T T        0 0 0 0 0   1,   . The payoff can be thought of as a function of V. 10 marks Question 4: (12 marks) The Chilean Pension Reserve Fund (PRF) was established on December 28, 2006 with an initial contribution of US$ 604.5 million by the Chilean Government. It was set up in response to Chile's new demographic scenario characterized by an increase in life expectancy and the growth of the senior citizen population, adding on yet another challenge for the Government in terms of greater future retirement expenditures and the need to guarantee basic solidarity pensions to those who were not able to save enough for their retirement. The PRF's objective is to support financing of government obligations arising from the government's guarantee to basic old age and disability solidarity pensions and solidarity pension contributions arising from the pension reform. Accordingly, this fund serves as a supplementary source for the funding of future pension contingencies. Pursuant to the Responsibility Law, PRF's capital increases each year by an amount equivalent to 0.2% of the previous year's gross domestic product (GDP). If the actual fiscal surplus exceeds 0.2% of GDP, the PRF receives a contribution equivalent to said surplus, up to a maximum of 0.5% of GDP. This accumulation rule allows for new resources to be allocated to the fund in any given year regardless of the fiscal situation facing the country each year. The spreadsheet "PRF – April 2016.xlxs" is available for download from iLearn and it contains a lot of information about the PRF. In particular5 it gives information about the asset allocation, the duration of the fixed income portfolio, currency exposure by asset class, details of the fixed income portfolio by credit rating and details of the asset classes by country / exchange rate exposure. By contrast, the Australian sovereign wealth fund (Future Fund) asset allocation at 31 March 2016 was as set out below. This is available at http://www.futurefund.gov.au/investment/investment‐performance/portfolio‐updates Asset Class A$m % of fund Australian equities 7,629 6.5% Global equities  Developed markets 17,899 15.2%  Emerging markets 8,594 7.3% Private equity 11,474 9.8% Property 8,316 7.1% Infrastructure & Timberland 8,330 7.1% Debt securities 13,314 11.3% Alternative assets 14,938 12.7% Cash 26,885 22.9% TOTAL 117,378 100.0% Write brief answers (up to 200 words) to each of the following questions (a) It is often said that equities provide an approximate hedge against inflation. Critique this suggestion and explain to what extent and over what time frame you think it is valid. To assess this, we can look at recent data, say the ten years to 30/6/2016. We can compute the return over each 3 month period ending on the last day of the months of March. June, September and December for both the CPI and the All Ordinaries Accumulation Index. See http://www.rba.gov.au/statistics/tables/#inflation‐expectations and download the file "g01hist.xls" for a history of the cpi inflation rate. See http://www.marketindex.com.au/all‐ordinaries and you can download the file "All Ordinaries (XAO).xlxs". 5 marks (b) Comment on the differences between the Future Fund's and the PRF's asset allocation and the exposure to different currencies based on the information supplied. Are the relative proportions of debt and equity and domestic vs foreign assets what you would expect given the purpose of the fund is to meet Chile's future retirement expenditures? Why ? 5 marks (c) What is a junk bond? In many countries, pension funds are prohibited from investing in bonds with a credit rating below investment grade. Why is this? Does it make sense? Does the PRF comply with this restriction? 3 marks6 (d) The PRF portfolio has a lot of assets from outside Chile. How would you respond to someone who says that the money should instead be invested domestically? What are the advantages and disadvantages of investing the PRF money in foreign assets? 3 marks (e) You are introduced to a new client with a $50m portfolio. Explain to the client, what "top down" asset allocation and "bottom up" stock selection are and how your fund's views, as opposed to that of other market participants, could provide value opportunities. 3 marks (f) Describe how you would go about establishing an appropriate "neutral" benchmark position (asset allocation) for their portfolio? If I have invested the portfolio at the benchmark allocations will this neutral position remain static? If not, how does the setting of asset class ranges ensure that the portfolio still reflects the client's risk profile. 3 marks (g) Investment managers' skills in investing in various asset classes is often judged relative to some index or benchmark. What are the features of a useful and valid benchmark for this purpose? 3 marks