A pension fund currently has $50 million in the S&P 500 index and $50 million in Treasury bills (risk-free asset). The current 6-month S&P 500 futures price is 1390.5, and one contract is on $250 times the index.
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Q: NAV
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- A ) A portfolio manager desires to generate $10 million 100 days from now from a portfolio that is quite similar in composition to the S&P 100 index. She requests a quote on a short position in a 100-day forward contract based on the index with a notional amount of $I0 million and gets a quote of $25.2. If the index level at the settlement date is $35.7. calculate the amount the manager will payor receive to settle the contract B) A forward contract covering a $10 million face value of T-bills that will have 100 days to maturity at contract settlement is priced at 1.96 on a discount yield basil. Compute the dollar amount the long must pay at settlement for the T-bills. C) Consider an FRA that: • Expires/settles in 30 days. • Is based on a notional principal amount of $1 million. • Is based on 9O-dayLIBOR. • Specifics a forward rate of 5%. Assume that the annual 9O-day LIBOR 30-days from now (at expiration) is 6%. Compute the cash settlement payment at expiration and identify which…A pension fund faces a promised outflow of $5 million in 6 years. Its managers plan to dedicate a portfolio comprised of the following two bonds to meet this obligation. a. What must be the proportions ((W7, W6) or (Weight(A), Weight(B)) of the two bonds in this 2-security portfolio to immunize it against changes in interest rates? b. What is the yield to maturity for the immunized portfolio? c. How much needs to be invested in each bond to build an immunized portfolio with an expected value of $5 million in 6 years? d. Suppose that it is now 3 years later and that there has been a parallel increase in interest rates of 2%. Explain how immunization at least partially protects this portfolio. That is, what are the sources of losses and gains associated with each of the bonds caused by the increase in interest rates? How do they offset each other?Suppose the 1-year futures price on a stock-index portfolio is 1,914, the stock index currently is 1,900, the 1-year risk-free interest rate is 3%, and the year-end dividend that will be paid on a $1,900 investment in the market index portfolio is $40.a. By how much is the contract mispriced?b. Formulate a zero-net-investment arbitrage portfolio and show that you can lock in riskless profits equal to the futures mispricing.c. Now assume (as is true for small investors) that if you short sell the stocks in the market index, the proceeds of the short sale are kept with the broker, and you do not receive any interest income on the funds. Is there still an arbitrage opportunity (assuming that you don’t already own the shares in the index)? Explain.d. Given the short-sale rules, what is the no-arbitrage band for the stock-futures price relation-ship? That is, given a stock index of 1,900, how high and how low can the futures price be without giving rise to arbitrage opportunities?
- = Consider the following DB pension plan: market value of assets $300 million, projected value of liabilities = $450 million, liability duration (i.e., duration of liabilities) = 10. If the portfolio manager wants to hedge interest-rate risk, what should be the duration of her portfolio? 13 12 15 14 0000You are an analyst for a large public pension fund and you have been assigned the task of evaluating two different external portfolio managers (Y and Z). You consider the following historical average return standard deviation, and CAPM beta estimates for these two managers over the past five years: Additionally, your estimate for the risk premium for the market portfolio is 5.00% and the risk-free rate is currently 4.50% c) Explain whether you can conclude from the info. In Part b if: (1) either manager outperformed the other on a risk-adjusted basis, and (2) either manager outperformed market expectations in general Portfolio Actual Avg.Return Standard Deviation Beta Manager Y 10.20% 12.00% 1.2 Manager Z 8.80% 9.90% 0.8Martin Brown is a fixed-income portfolio manager who works with large institutional clients. Brown is meeting with Sarah Redi, a consultant to the Horizon Redi Pension Plan, to discuss the management of the fund's, approximately R100 million. Treasury bond portfolio. The current Treasury yield curve is given in the following table. Maturity (years) 1 12 3 4 YTM (%) 6.0 8.0 9.0 9.5 Assume that the liquidity premiums for the one-year, two-year and three-year maturities (one year from now) are 1% 2.33% and 4%, respectively, determine the expected spot rates in one years time for the one, two, and three year maturing bonds.
- The manager of a well-diversified portfolio with a market value of $200 million that mirrors the S&P 500 wants to hedge the portfolio against a market decline in value over the next six months. The portfolio manager wants to use the Mini-S&P 500 contract for hedging. The contract multiplier for this futures contract is $50. The futures price for the contract at the date that the hedge is put on is 4,200. a. Should the portfolio manager buy or sell the futures contract. Explain why. b. How many contracts should the portfolio manager sell or buy? c. Suppose at the delivery date (six months from now), the value of the S&P 500 is 3,800. Show what the outcome for this hedge will be.At time t=0 Mr. Anderson sets up a riskless portfolio by taking a position in an option and in the underlying asset. Explain what Mr. Anderson needs to do at time t=1 to keep his portfolio risk neutral and why. A stock price is currently $100 and at the end of four months it will be ST . A derivative written on this stock pays off expST1/3 in four months. Given that u = 1.15, d = 0.87, and that the risk-free interest rate is 10% p.a. (continuously compounded), answer the following questions using a one-period binomial model (show all the details of your calculations and display the results with four decimal places): Calculate the value of ∆ Calculate the current value of the derivative.A fund manager has a portfolio worth $95 million with a beta of 1.16. The manager is concerned about the performance of the market over the next two months and plans to use three-month futures contracts on the S&P 500 to hedge the risk. The current level of the S&P 500 index is 2,675, the risk-free rate is 2% per annum, and the dividend yield on the index is 4% per annum. The current 3-month S&P 500 index futures price is 2,660, and one contract is on 250 times the index. (a) What position should the fund manager take to eliminate all risk exposure to the market over the next two months? (B' = 0) How many three-month S&P 500 futures contracts should the fund manager buy or sell now? (Rounding to the nearest whole number.) (b) Calculate the effect of your strategy on the fund manager's returns if the level of the S&P 500 index in two months is 2,585. Assume that the 3-month S&P 500 index futures price is 2,570 in two months. What would be the expected value of the fund manager's hedged…
- You are an analyst for a large public pension fund and you have been assigned the task of evaluating two different external portfolio managers (Y and Z). You consider the following historical average return standard deviation, and CAPM beta estimates for these two managers over the past five years: Additionally , your estimate for the risk premium for the market portfolio is 5.00% and the risk-free rate is currently 4.50% a) For both Manager Y and Manager Z, calculate the expected return using the CAPM, Express your answers to the nearest basis point (i.e. xx.xx%) Portfolio Actual Avg.Return Standard Deviation Beta Manager Y 10.20% 12.00% 1.2 Manager Z 8.80% 9.90% 0.8Consider a portfolio manager with a $20,500,000 equity portfolio under management. The manager wishes to hedge against a decline in share values using stock index futures. Currently a stock index future is priced at 1250 and has a multiplier of 250. The portfolio beta is 1.25. Calculate the number of contract required to hedge the risk exposure and indicate whether the manager should be short or long. 82 contracts long. 100 contract short. 82 contracts short. 100 contracts long.Suppose that a portfolio management company manages an investment fund. The fund manager observes a bond in the market and intends to add it to the fund portfolio. The bond has a 100.000 TL par value, 10% coupon rate (coupon payments are annual) and a 2-years maturity. The business model is to “hold-until-maturity”. The company purchases the bond at the beginning of the year when the market yields are 12%. After exactly 1 year of investment, market yields increase to 14%. What would be the approximate profit or loss amount in the income statement for that 1-year period? A) 1.723 TL loss B) 10.191 TL profit C) 9.871 TL profit D) 1.594 TL loss E) OTHER