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FIXED-INCOME PORTFOLIO MANAGEMENT—PART II CHAPTER 12 © 2016 CFA Institute. All rights reserved. TABLE OF CONTENTS 06 OTHER FIXED-INCOME STRATEGIES 07 INTERNATIONAL BOND INVESTING 08 SELECTING A FIXED-INCOME MANAGER 09 SUMMARY 2 6. OTHER FIXED-INCOME STRATEGIES • Frequently, a manager is permitted to use leverage as a tool to help increase the portfolio’s return. Example: Assume that a manager has $40 million of funds to invest. The manager then borrows an additional $100 million at 4% interest. All of the funds can be invested at a 4.5% rate of return. Calculate the returns on the portfolio’s components: Borrowed Funds Amount invested Equity Funds $100,000,000 $40,000,000 Rate of return at 4.5% 4,500,000 1,800,000 Less interest expense at 4% 4,000,000 0 500,000 1,800,000 Net profitability 3 OTHER FIXED-INCOME STRATEGIES Example (continued). • Rate of return on borrowed funds $500,000 = 𝟎. 𝟓𝟎% $100,000,000 • Rate of return on equity funds (without leverage) $1,800,000 = 𝟒. 𝟓𝟎% $40,000,000 • Rate of return on equity funds (with leverage) $1,800,000 + $500,000 = 𝟓. 𝟕𝟓% $40,000,000 The return on equity increased by 1.25% with leverage. The larger the amount of borrowed funds, the larger the magnification will be (positive or negative). 4 LEVERAGE • If E = amount of equity; B = amount of borrowed funds; k = cost of borrowing; rF = return on funds invested; and RB, RE, and RP are returns on borrowed funds, equity, and portfolio, then: 𝑹𝑩 = 𝒓𝑭 − 𝒌 𝑹𝑬 = 𝒓𝑭 𝑹𝑷 = 𝒓𝑭 + 𝑩 𝑬 × (𝒓𝑭 − 𝒌) • The duration of the levered equity portfolio is: 𝑫𝑨 𝑨 − 𝑫𝑳 𝑳 𝑫𝑬 = 𝑬 where A = assets (bond portfolio); L = liabilities (borrowed funds); and DA, DL, and DE = durations of assets, liabilities, and equity. 5 REPURCHASE AGREEMENTS Among investment managers’ favorite instruments to increase the leverage of their portfolios is the repo. A repurchase agreement is a contract involving the sale of such securities as Treasury instruments coupled with an agreement to repurchase the same securities on a later date. The repo market presents a low-cost way for managers to borrow funds by providing Treasury securities as collateral. The repo agreements typically have short terms to maturity. 6 REPURCHASE AGREEMENTS Quality of the collateral Seasonal factors Prevailing interest rates in the economy Term of the repo A variety of factors will affect the repo rate, including: Delivery requirement Availability of collateral 7 PORTFOLIO RISK MEASURES Portfolio risk can be described by the following statistical measures: Standard deviation measures the dispersion of data from its mean, assuming a normal distribution. Semi variance measures the dispersion of return outcomes that are below the target return. Shortfall risk is the probability of not achieving some specified return target. Value at risk (VAR) is an estimate of the $ loss that the portfolio manager expects to be exceeded with a given level of probability over a specified time period. 8 PORTFOLIO RISK MEASURES The deficiencies of the statistical measures are: Standard deviation • has an unrealistic assumption of a normal distribution of returns, especially for portfolios having securities with embedded options. Semivariance • is computationally challenging for large portfolios, adds no value for the symmetric returns, is difficult to forecast for asymmetric returns, and uses only half of observations, which reduces its statistical accuracy. Shortfall risk • does not account for the magnitude of losses in money terms. VAR • does not indicate the magnitude of the very worst possible outcomes. 9 INTEREST RATE FUTURES • A futures contract is a contract between a buyer (seller) and an established exchange or its clearinghouse in which the buyer (seller) agrees to take (make) delivery of the underlying asset at a specified price at the specified time. • There are a number of advantages to using futures contracts rather than the cash markets for purposes of portfolio duration control: + • Liquidity and cost-effectiveness • Shorting (selling) the contract for effective duration reduction 10 DURATION MANAGEMENT A portfolio’s dollar duration can be changed with futures contracts so that it equals a specific target duration. Portfolio’s target dollar duration Dollar duration of futures Current portfolio’s dollar duration without futures Dollar duration of each futures contract Dollar duration of the futures contracts Number of futures contracts (𝐷𝑇 −𝐷𝐼 )𝑃𝐼 alternatively, Dollar duration per futures contract 𝐷𝑇 −𝐷𝐼 𝑃𝐼 × Conversion factor for the CTD bond 𝐷𝐶𝑇𝐷 𝑃𝐶𝑇𝐷 𝑵𝑭 ≈ 𝑵𝑭 ≈ where DT, DI, and DCTD = target, initial, and cheapest-to-deliver (CTD) bond durations; PT and PCTD = market value of the portfolio and the price of the CTD bond. 11 DURATION MEASUREMENT WITH FUTURES Example: The market value of a UK pension fund’s bond portfolio is £50 million. The portfolio’s duration is 9.52. Expecting an increase in interest rates, the pension fund decided to reduce duration to 7.5 by using a futures contract priced at £0.1 million that has a duration of 8.47. Assume a conversion factor of 1.1. Calculate the number of contracts required for the change in duration. 7.5 − 9.52 × 50,000,000 𝑁𝐹 ≈ × 1.1 = −𝟏𝟑𝟏. 𝟕 8.47 × 100,000 The pension fund would need to sell 131 futures contracts. 12 DURATION HEDGING • Hedging with futures contracts involves taking a futures position that offsets an existing interest rate exposure. The key to minimizing risk in a cross hedge is to choose the right hedge ratio. 𝐇𝐞𝐝𝐠𝐞 𝐫𝐚𝐭𝐢𝐨 = 𝐇𝐞𝐝𝐠𝐞 𝐫𝐚𝐭𝐢𝐨 = Factor exposure to be hedged Factor exposure of futures contract 𝐷𝐻 𝑃𝐻 𝐷𝐶𝑇𝐷 𝑃𝐶𝑇𝐷 alternatively, × Conversion factor for the CTD bond where DH and PH = duration and price of the bond to be hedged. 13 DURATION HEDGING A hedger can use regression analysis to capture the relationship between yield levels and yield spreads. Yield on bond to be hedged = a + b(Yield on CTD bond) + Error term where the estimate of b, called the yield beta, is the expected relative change in the two bonds. The hedge ratio with yield beta is 𝑯𝑹 = 𝐷𝐻 𝑃𝐻 𝐷𝐶𝑇𝐷 𝑃𝐶𝑇𝐷 × Conversion factor for the CTD bond × Yield beta 14 INTEREST RATE SWAPS An interest rate swap can be used to alter the cash flow characteristics of an institution’s assets or liabilities so as to provide a better match between assets and liabilities. An interest rate swap is a contract between two parties to exchange periodic interest payments based on a specified dollar amount of principal. The traditional swap has one party making periodic payments at a fixed rate in return for the counterparty making periodic payments based on a benchmark floating rate. For a floating-rate payer, the dollar duration (DD) of a swap is: 𝐃𝐃 𝐬𝐰𝐚𝐩 = DD fixed rate bond − DD floating rate bond 15 BOND AND INTEREST RATE OPTIONS Options can be used to hedge a bond portfolio. Options on futures give the buyer the right to buy from or sell to the writer a designated futures contract at the strike price at a specified time during the life of the option. The price of a bond option will depend on the price of the underlying instrument, which depends in turn on the interest rate on the underlying instrument. The duration of an option (Do) is: 𝑫𝒐 = δ × 𝐷𝑢 × 𝑃𝑢 𝑃𝑜 where Du and Pu = duration and the price of the underlying; δ and Po = delta and the price of the option. 16 HEDGING WITH OPTIONS There are two hedging strategies in which options are used to protect against a rise in interest rates: Protective put buying establishes a minimum value for the portfolio but allows the manager to benefit from a decline in rates. In covered call writing, the covered call writer sells outof-the-money calls against an existing bond portfolio to generate premium income that provides partial protection in case rates increase. Interest rate caps and floors can assist in setting the ceiling and the floor for short-term borrowing rates. 17 CREDIT RISK INSTRUMENTS Derivatives can help with hedging credit risks. • There are three types of credit risk: Default risk is the risk that the issuer may fail to meet its obligations. Credit spread risk is the risk that the spread between the rate for a risky bond and the rate for a default riskfree bond (like US Treasury securities) may vary after the purchase. Downgrade risk is the risk that one of the major rating agencies will lower its rating for an issuer based on its specified rating criteria. 18 CREDIT OPTIONS • There are variety of credit derivatives, including the following: Credit options • The triggering events of credit options can be based either on: (1) the value decline of the underlying asset or (2) the spread change over a risk-free rate. • For the latter, the credit spread option can be used. Credit spread options are call options in which the payoff is based on the spread over a benchmark rate. The payoff (for a call option) is: 𝐏𝐚𝐲𝐨𝐟𝐟 = Max Spread at maturity − 𝐾 × 𝑁 × 𝑅𝐹, 0 Credit forward • The buyer of a credit forward contract benefits from a widening credit spread, and the seller benefits from a narrowing credit spread. Payoff for the buyer is: 𝐏𝐚𝐲𝐨𝐟𝐟 = Spread at maturity − Contracted credit spread × 𝑁 × 𝑅𝐹 where N = notional amount; RF = risk factor; K = strike spread. 19 CREDIT OPTIONS - Credit swaps. A number of different products can be classified as credit swaps. The credit default swap is the most popular. - A credit default swap is a contract that shifts credit exposure of an asset issued by a specified reference entity from one investor (protection buyer) to another investor (protection seller). - The protection buyer usually makes regular payments — the swap premium payments (default swap spread) — to the protection seller. Swap premium Protection buyer Payment on credit event Protection seller 20 7. INTERNATIONAL BOND INVESTING • The motivation for international bond investing (i.e., investing in nondomestic bonds) includes portfolio risk reduction and return enhancement. The opportunities for active management are created by inefficiencies that may be attributed to the following: • Differences in tax treatment • Local regulations and coverage by fixed-income analysts • Differences in how market players respond to similar information The active manager seeks to exploit those inefficiencies through the following: • Superior bond market selection • Currency selection • Duration management/yield curve management • Sector selection • Credit analysis of issuers • Investing outside the benchmark index 21 RELATIONSHIP BETWEEN DURATION OF FOREIGN BOND AND INVESTOR’S PORTFOLIO • Thomas and Willner (1997) suggested the following methodology for computing the contribution of a foreign bond’s duration to the duration of a portfolio: ∆ 𝑽𝑭𝑩 = −Duration × ∆Yield𝐹 × 100 or ∆ 𝑽𝑭𝑩 = −Duration × ∆Yield𝐹 given ∆Yield𝐷 × 100 The relationship between ∆𝐘𝐢𝐞𝐥𝐝𝑭 and ∆𝐘𝐢𝐞𝐥𝐝𝑫 is estimated ∆𝐘𝐢𝐞𝐥𝐝𝑭,𝒕 = α + β∆Yield𝐷,𝑡 where ∆ 𝑽𝑭𝑩 = change in value of the foreign bond; ∆𝐘𝐢𝐞𝐥𝐝𝑭,𝒕 and ∆𝐘𝐢𝐞𝐥𝐝𝑫,𝒕 = changes in values of foreign and domestic yields at time t; 𝛃 = correlation (∆Yield𝐹,𝑡 , ∆Yield𝐷,𝑡 ) × σ𝐹 /σ𝐷 . 22 CURRENCY RISK Every investor in foreign markets can either remain exposed to this currency risk or hedge it. - Unhedged return is equal to: 𝑹 ≈ 𝒓𝒍 + 𝒆 - Hedged return is equal to: 𝑯𝑹 ≈ 𝒓𝒍 + 𝒇 ≈ 𝒓𝒍 + 𝒊𝒅 − 𝒊𝒇 = 𝒊𝒅 + (𝒓𝒍 − 𝒊𝒇 ) where 𝒓𝒍 = local currency return of the foreign bond; 𝒆 = the currency return; 𝒊𝒅 and 𝒊𝒇 = domestic and foreign risk-free rate. 23 BREAKEVEN SPREAD ANALYSIS Breakeven spread analysis can be used to quantify the amount of spread widening required to diminish a foreign yield advantage. The breakeven spread widening analysis must be associated with an investment horizon (e.g., 3 months) and must be based on the higher of the two countries’ durations. Duration plays an important role in breakeven spread analysis. The analysis ignores the impact of currency movements. 24 EMERGING MARKET DEBT • Emerging market debt (EMD) includes sovereign bonds as well as debt securities issued by public and private companies in those countries. • Recently, emerging market debt has matured as an asset class and now frequently appears in many strategic asset allocations because of: • High return potential • Favorable diversification properties 25 EMERGING MARKET DEBT Risks do exist in the EMD sector: • Volatility in the EMD market is high. • EMD returns are frequently characterized by significant negative skewness. • The EMD market does not offer the degree of transparency, court-tested laws, and clear regulations found in established markets. • There is less protection from interference by the governments. • Emerging countries tend to over borrow. • Recovery against sovereign states can be very difficult. • There is little standardization of covenants. 26 8. SELECTING A FIXED-INCOME MANAGER • When funds are not managed entirely in-house, a search for outside managers must be conducted. • The due diligence for selection of managers is satisfied primarily by investigating the following: • Managers’ investment process • Types of trades the managers are making • Managers’ organizational strengths and weaknesses. • The aim is to find managers who can produce consistent positive styleadjusted alphas. • Then, a combination of managers is optimized based on their styles and exposures. 27 9. SUMMARY Effect of leverage on duration and investment returns • Leverage has a magnifying effect on a portfolio’s risk and return. Repurchase agreements • The repurchase agreements market is an important and cost-effective source of funds to finance bond purchases. • Factors affecting the repo rate are quality of the collateral, term of the repo, delivery requirement, availability of collateral, prevailing interest rates in the economy, and seasonal factors. Statistical measures of fixed-income portfolio risk • Standard deviation, target semivariance, shortfall risk, and value at risk have all been proposed as appropriate measures of risk for a portfolio. However, each has its own deficiency. 28 SUMMARY Advantages of using futures • The primary advantages to using futures to alter a portfolio’s duration are increased liquidity and cost-effectiveness. Immunization strategy based on interest rate futures • Futures contracts can be used to shorten or lengthen a portfolio’s duration. • The contracts may also be used to hedge or reduce an existing interest rate exposure. Use of interest rate swaps and options • Interest rate swaps and options can also be used to hedge interest rate risk. • Swaps are flexible and cost-effective instruments. 29 SUMMARY Use of credit derivative instruments • Credit options are structured to offer protection against both default risk and credit spread risk; credit forwards offer protection against credit spread risk; and credit default swaps help in managing default risk. Sources of excess return for an international bond portfolio • The sources of excess return for an international bond portfolio include bond market selection, currency selection, duration management/yield curve management, sector selection, credit analysis, and investing in markets outside the benchmark index. 30 SUMMARY Effect of change in value for a foreign bond • For a change in domestic interest rates, the change in a foreign bond’s value may be found by multiplying the duration of the foreign bond times the country beta. • Because a portfolio’s duration is a weighted average of the duration of the bonds in the portfolio, the contribution to the portfolio’s duration is equal to the adjusted foreign bond duration multiplied by its weight in the portfolio. Hedging of a currency risk • The decision about how much currency risk to hedge—from none to all—is important because currency movements can have a dramatic effect on the investor’s return from international bond holdings. 31 SUMMARY Breakeven spread analysis • Breakeven spread analysis is used to estimate relative values between markets by quantifying the amount of spread widening required to reduce a foreign bond’s yield advantage to zero. Advantages and risks of investing in emerging market debt • The quality of sovereign bonds has increased to the point that they now have similar frequencies of default, recovery rates, and ratings transition probabilities compared with corporate bonds with similar ratings. • Emerging market debt is still risky, however, and is characterized by high volatility and returns that exhibit significant negative skewness. Moreover, emerging market countries frequently do not offer the degree of transparency, court-tested laws, and clear regulations found in established markets. 32 SUMMARY Criteria for selecting a fixed-income manager • When funds are not managed entirely in-house, a search for outside managers must be conducted. • The due diligence for selection of managers is satisfied primarily by investigating the managers’ investment process, the types of trades the managers are making, and their organizational strengths. 33