EXAMINATION II: Fixed Income Valuation and Analysis. Derivatives Valuation and Analysis. Portfolio Management

Transcription

1 EXAMINATION II: Fixed Income Valuation and Analysis Derivatives Valuation and Analysis Portfolio Management Questions Final Examination March 2011

2 Question 1: Fixed Income Valuation and Analysis (43 points) You are the Head of Debt Issuance of a European bank which 10 years ago issued the following perpetual subordinated fixed income bond with a coupon step-up if not called. The call is a one-time option which is available 10 years after the bond issue (i.e. today). : Security Issue Price Issue Volume Coupon (fix) Maturity Call Date /strike Subordinated 100% 1bn 5% perpetual today bond p.a. /100% Notes: bps = Basis Points : 1 bps = 0.01%; yield convention: 30/360. Step-up +100 bps p.a. Spread over swap yield 425 bps p.a. The yield spread of the bond widened significantly in the light of turbulence in the financial markets. As a result you have to deal with the question of calling the security vs. not calling it and thus incurring the aforementioned coupon step-up. You are asked to advise your Management Board on the future treatment of this security. a) To start with, you are confronted with some basic questions (assuming that the call option is not exercised). a1) Calculate the current price of the aforementioned bond at the relevant swap rate of 3.50% p.a. (4 points) a2) Determine the modified duration of the given perpetual bond. (4 points) The Macaulay Duration D of a perpetual bond is defined as follows: 1 D 1 Yield a3) Approximate the price of the given bond after a spread tightening of 100bps using a duration based approach. [Note: use a bond price of 65% and a Macaulay Duration of 14 years in case you have not solved questions a1) & a2).] (4 points) a4) Do you consider the approximation in question a3) as being reliable? Explain. b) You are now asked to conduct a cost/benefit-analysis on the call vs. non-call decision. b1) Assume that this perpetual bond position is marked to market. Calculate the direct economic loss (in EUR millions) when calling the bond today at 100%. (Note: Assume that the liquidity outflow due to the call does not have to be replaced by new issuances and that all other market parameters given in a) above are assumed to be constant. Use a bond price of 65% in case you have not solved question a1).) (4 points) b2) Calculate the break-even spread over swap yield that makes the economic loss (mentioned under b1) equal to zero. (3 points) Page 1 / 9

3 b3) Assume now that the perpetual bond would have to be replaced after its call by a 30-year bond with a 7% p.a. coupon rate. Calculate the present value of the additional interest expenses. [Hint: compare the interest expenses p.a. of the new 7% bond vs. those of the perpetual after step-up and translate the result into a present value over 30 years at a discount rate of 7%.] b4) Provide two reasons in favor of calling the bond despite the fact that the embedded call option is out-of-the-money. (No calculation required only short answers in bullet point style required) (4 points) c) Lastly, you are asking two brokers A and B for pricing a new perpetual bond, callable in 10 years: although both brokers A and B indicate the same price, as far as volatility of embedded call option is concerned, Broker A quotes you 20% whereas Broker B comes up with only a 10% volatility. c1) Which broker offer implies the higher Option-Adjusted-Spread (OAS)? (No calculation required only short reasoning required.) c2) How do you view the convexity of the given callable perpetual bond compared to a bond without a call feature? (No calculation required only short reasoning required) Page 2 / 9

4 Question 2: Derivatives Valuation and Analysis (27 points) As a portfolio manager of a USD based Bond Fund you are interested in investing in some Government Bonds denominated in EUR with short-term maturities (maximum 3 years). You have at your disposal the following risk-free interest rates (p.a.) for the EUR and the USD for different maturities. Overnight 3 months 6 months 1 year 3 years EUR 1% 1.25% 1.50% 1.75% 2% USD 2% 1.75% 1.50% 1.25% 1% The current spot exchange rate is 1 EUR = 1.40 USD or EUR/USD You decide to buy a Government Bond with a maturity of 3 years for an amount of 20 million EUR and decide to hedge your portfolio back to USD: a) Calculate the forward exchange rate EUR/USD for 6 months using the information above. (4 points) b) Compare the spot and the forward exchange rates providing explanations for the result. c) You decide to use currency futures to hedge against the EUR. After a shock in interest rates, the HR (hedge ratio) between the spot and the future moves to Using this new hedge ratio, calculate the number of future contracts you need to hedge in order to maintain a perfect hedge (1 contract = 125,000 EUR). What would the impact be were the hedge ratio not to be adjusted to this new ratio? (No calculations required)? (7 points) d) Calculate the implied forward rate for a 6-months deposit starting in 6-months from the above interest rate curves for the USD and the EUR. (Use 30/360 day count convention.) e) Comment on the shape of the USD and EUR yield curve shown above. What factors influence in general the shape of the yield curve? List four of them. (6 points) Page 3 / 9

5 Question 3: Derivatives Valuation and Analysis (20 points) This problem considers the spread for 5-year CDSs issued on Company A between April 2009 and March a) During this period, Company A's CDS spread was rising. List two general factors behind the CDS rise. b) In March 2010, Company A's 5-year corporate bond has a yield of 3%, while a 5-year government bond has a yield of 1%. Assuming that there are no arbitrage opportunities in the market at this time, what is the theoretical value (as a percentage) of the 5-year CDS spread on Company A? (4 points) c) With the yields as given in question b) [i.e. Company A's 5-year corporate bond yields 3%, while a 5-year government bond yields 1%], the actual value of Company A's 5-year CDS spread observed on the market is 2.5%. So, there are arbitrage opportunities. Describe the arbitrage trades. d) As can be seen from Questions b) and c), there may be a difference between the theoretical CDS spread and the actual CDS spread observed in the market. Why is this the case? Describe three possible reasons. (6 points) Page 4 / 9

6 Question 4: Portfolio Management (50 points) You have been given the job as chief investment officer of a pension fund. You are trying to optimize the overall financial structure as well as some special segments of the fund. a) A large section of your overall portfolio ( core ) is allocated to passive equity investment. You want to assess some basic methodological issues. Define the following tracking approaches - stratified sampling - sampling by eliminating the stocks with smallest benchmark weight and - optimised sampling (9 points) b) Comparing these three indexing approaches, what are the general advantages and disadvantages of each approach? (9 points) c) For another section of the fund, active management of global emerging markets equities, you receive a RFI ( request for interest ) of M1, an active equity manager, that offers its portfolio management services to you. Find below an excerpt of the RFI, where the portfolio construction methodology is outlined (for ease of further reference, the sentences are numbered): (1) We strongly believe in active management on the basis of the Fundamental Law of Active Management. At the core of our investment process is a market timing model, that produces quarterly forecasts about the direction of the overall equity market. As this model has a good hit ratio (and hence a good performance), we do not engage in other active elements other than market timing. For stock selection we use an indexing approach. (2) As we use variance/covariance forecasts for the indexing, our indexing approach is very robust. (3) The formal optimization problem that we solve is: P,B V ~ P,B max E(R A ) v (R A ) (the difference between the expected return and v times the active variance or the square of the expected tracking error) as a function of w (the portfolio weights) with P i N i 1 P w i 0 (all portfolio weights have to add up to zero) and an additional constraint, that limits the number of stocks in the portfolio to a positive number N P. P,B [Note: R A active return of the portfolio relative to its benchmark. w weight for each asset i in a portfolio.] P i (4) The parameter v allows us to express how much we value the forecasted risk in terms of returns. Page 5 / 9

7 (5) By increasing v, we can tilt the trade-off between risk and return in favour of taking risks. (6) As a separate strategy we can offer you our Enhanced Indexing variant. We use two components for enhancement: the options overwriting approach as well as tilting the portfolio to make use of the earnings surprise anomaly, which is based on the empirical fact, that contrary to intuition stocks with published earnings that are better than expected, tend to underperform directly after publication. (7) This option overwriting component yields incremental returns compared to purely passive indexing. (8) This option-based enhancement element is very robust, since it is not based on return forecasts. (9) The realized outperformance (annualized) of our active approach is 3.3% p.a. over the last 3 years (with a tracking error of 3% p.a.). You are astonished by the quality of this description. List the numbers of 5 statements, which strike you as wrong, and give reasons for each assessment. (10 points) d) You receive another RFI from an active asset manager ( M2 ). The RFI contains a table with realized active returns for the last 108 months. These monthly active returns have an arithmetic mean of 0.25% (after costs) and a standard deviation of 0.9% (both numbers not annualized i.e. they are calculated on a monthly basis). Calculate the realized annualized information ratio for M2 as well as for M1 (from c). Is M2 s track record superior? Explain. (8 points) e) Describe the Core/Satellite approach of constructing an overall portfolio, mixing active and passive sub-mandates. Define the major advantages/disadvantages compared to an approach that mixes generalist balanced mandates. (9 points) f) After an intensive asset manager search, you pick 3 asset managers, that will manage against the following benchmarks: Al1: Global Equity Index (passive) Al2: Global Equity Index (active) Al3: Global Government Bond Index (passive) The expected active returns, tracking errors and the management fees of all managers can be found in the following table: Manager Active return Tracking error Management fees (before fees) Al1 0.03% 0.20% 0.05% Al2 3.50% 5.00% 0.40% Al3 0.00% 0.10% 0.03% Page 6 / 9

8 The strategic asset allocation of the fund is 50% equities and 50% bonds. You want to achieve an expected active return of 1.5% after costs. What percentages of your overall portfolio do you have to allocate to these 3 managers for achieving the desired result? Page 7 / 9

9 Question 5: Derivatives and Derivatives in Portfolio Management (40 points) The Nikkei average is currently 10,000 yen and the risk-free rate 4% (annualized). Futures and options with the same underlying assets as the Nikkei average are traded. You have been assigned to manage a (diversified) stock portfolio with the same composition as the Nikkei average and a present value of 1 billion yen, and have been asked to add derivatives trading to boost investment returns. You are required to answer the following questions. For the sake of simplicity, you may ignore dividends. All futures and options mature 3 months from now and 1 trading unit is 1,000 times the Nikkei average. (That is, the cost of purchasing 1 trading unit of options is 1,000 times the option price.) Options are European style. The strike prices of traded puts are 8,000, 9,000 and 10,000 yen; the strike prices of calls are 10,000, 11,000 and 12,000 yen. a) Find the theoretical current futures price. (Show the equation used to derive it.) (4 points) b) The current price of a call option with a strike price of 10,000 is 665 yen; a put option with the same 10,000 strike price has a current price of 545 yen. You have found an arbitrage opportunity. Explain why this is an arbitrage opportunity, provide an example of an arbitrage trade showing how many units of what asset should be traded at the current point in time in order to profit from the arbitrage, and find the profit to be gained from the trade. (10 points) c) The arbitrage opportunity described in b) above quickly disappeared, but there is greater uncertainty in the market and expectations that there will be either a large drop or a large rise in the Nikkei average over the very near term. Provide a specific proposal for how many units of what kinds of options to trade to create a position that will allow you to profit from these expectations. Draw a payoff diagram for the position at maturity and explain why you expect to profit. (8 points) Payoff 0 Value of the Nikkei average at maturity Page 8 / 9

10 d) The forecast described in c) above is corrected and there is now strong concern that the Nikkei average will decline over the coming 3 months. You want to maintain the value of your fund above a constant level in 3 months time and therefore decide to set a floor by purchasing put options with strike price K that have the current price P K. To do this, you borrow the funds for purchasing the options at the risk-free rate and repay them in 3 months time. If the value of the Nikkei average at maturity is below the strike price K, the value of the fund will be maintained at a constant level thanks to the put options. Find the number of units of options to be purchased in order to set up the floor and use the option price and strike price to express the value of the floor established. Draw a payoff diagram showing the value of all positions (total of stock portfolio, options and risk-free rate borrowing) on the vertical axis and the value of the Nikkei average on the horizontal axis after 3 months. (7 points) Position value 0 Value of the Nikkei average e) You can add a call option trade to raise the floor value established in d). How should you trade call options to do this? How will the value of all positions after 3 months change (in comparison to d)) by adding this trade? Briefly discuss the costs and benefits of this call option trade. There is no need to perform calculations. f) As a result of the investigations in d), you learn that a desirable floor can be achieved by purchasing the following put options, but instead of purchasing the options you decide to perform dynamic hedging by the futures to synthesize the same payoff. Strike price K Put option price P K Delta 9, Find the futures position you should take at this point in time to synthesize the option. Explain how the futures position should be adjusted in the future in reaction to a fall or rise in the Nikkei average in order to maintain dynamic hedging. (6 points) Page 9 / 9