Reading 22 Fixed-Income Portfolio Management—Part II

Question 1

Interest Rate Parity

Answer 1

• Interest rate parity (IRP) states that the forward foreign exchange rate discount or premium over a fixed period should equal the risk-free interest rate differential between the two countries over that period to prevent the opportunity for arbitrage profits using spot and forward currency markets plus borrowing or lending.
• The currency quotation convention used — domestic currency/foreign currency — called direct quotation, means that from the perspective of an investor in a foreign asset an increase in the spot exchange rate is associated with a currency gain from holding the foreign asset. According to IRP,

f (forward discount or premium) ≈ i_d – i_f

Question 2

Repurchase Agreements

Answer 2

• A** repurchase agreement **is a contract involving the sale of securities such as Treasury instruments coupled with an agreement to repurchase the same securities on a later date. The importance of the repo market is suggested by its colossal size, which is measured in trillions of dollars of transactions per year.
• The repo transaction functions very much like a collateralized loan. In fact, the difference in selling price and purchase price is referred to as the “interest” on the transaction.
• RP agreements typically have short terms to maturity, usually overnight or a few days, although longer-term repos of several weeks or months may be negotiated. If a manager wants to permanently leverage the portfolio, he may simply “roll over” the overnight loans on a permanent basis by entering the RP market on a daily basis.

Question 3

Credit Risk Instruments

Answer 3

• A given fixed-income security usually contains several risks. The interest rate may change and cause the value of the security to change (interest rate risk); the security may be prepaid or called (option risk); and the value of the issue may be affected by the risk of defaults, credit downgrades, and widening credit spreads (credit risk).
• Credit risk can be sold to another party. In return for a fee, another party will accept the credit risk of an underlying financial asset or institution. This party, called the credit protection seller, may be willing to take on this risk for several reasons. Perhaps the credit protection seller believes that the credit of an issuer will improve in a favorable economic environment because of a strong stock market and strong financial results. Also, some major corporate events, such as mergers and acquisitions, may improve corporate ratings. Finally, the corporate debt refinancing caused by a friendlier interest rate environment and more favorable lending rates would be a positive credit event.
• There are three types of credit risk: default risk, credit spread risk, and downgrade 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 risk-free 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.
• A variety of derivative products, known as credit derivatives, exist to package and transfer the credit risk of a financial instrument or institution to another party.

Question 4

Risk and Return Characteristics of EMD

Answer 4

Sovereign emerging market governments possess several advantages over private corporations:

• They can react quickly to negative economic events by cutting spending and raising taxes and interest rates.
• They also have access to lenders on the world stage, such as the International Monetary Fund and the World Bank.
• Many emerging market nations also possess large foreign currency reserves.

Risks do exist in the sector however:

• Volatility in the EMD market is high.
• EMD returns are also frequently characterized by significant negative skewness. Negative skewness is the potential for occasional very large negative returns without offsetting potential on the upside.
• Emerging market countries frequently do not offer the degree of transparency, court-tested laws, and clear regulations that developed market countries do. The legal system may be less developed and offer less protection from interference by the executive branch than in developed countries. Also, developing countries have tended to over borrow, which can damage the position of existing debt.
• Little standardization of covenants exists among various emerging market issuers
• Investors in EMD face default risk as does any investor in debt. Sovereign EMD bears greater credit risk than developed market sovereign debt, reflecting less-developed banking and financial market infrastructure, lower transparency, and higher political risk in developing countries. Rating agencies issue sovereign ratings that indicate countries’ ability to meet their debt obligations. Standard & Poor’s investment-grade sovereign rating of BBB– and Moody’s Baa3 are given to the most credit-worthy emerging markets countries.
• ! Sovereign debt also typically lacks an enforceable seniority structure, in contrast to private debt.

Question 5

Duration Hedging

Answer 5

• Hedging with futures contracts involves taking a futures position that offsets an existing interest rate exposure. If the hedge is properly constructed, as cash and futures prices move together any loss realized by the hedger from one position (whether cash or futures) will be offset by a profit on the other position.
• The difference between the cash price and the futures price is called the basis. The risk that the basis will change in an unpredictable way is called basis risk.
• In some hedging applications, the bond to be hedged is not identical to the bond underlying the futures contract. This kind of hedging is referred to as cross hedging. There may be substantial basis risk in cross hedging, that is, the relationship between the two instruments may change and lead to a loss. An unhedged position is exposed to price risk, the risk that the cash market price will move adversely. A hedged position substitutes basis risk for price risk.
• Conceptually, cross hedging requires dealing with two additional complications. The first complication is the relationship between the cheapest-to-deliver security and the futures contract. The second is the relationship between the security to be hedged and the cheapest-to-deliver security.
• The key to minimizing risk in a cross hedge is to choose the right hedge ratio.
• The relevant point in the life of the bond for calculating exposure is the point at which the hedge will be lifted. Exposure at any other point is essentially irrelevant
• In the discussion so far, we have assumed that the yield spread is constant over time. In practice, however, yield spreads are not constant over time. The regression procedure provides an estimate of b, called the yield beta, which is the expected relative change in the two bonds.
• The formula for the hedge ratio can be revised to incorporate the impact of the yield beta by including the yield beta as a multiplier.

Hedge ratio = (D_HP_H)/(D_CTDP_CTD) × Conversion factor for the CTD bond × Yield beta

Question 6

Duration Management

Answer 6

The number of futures contracts that is needed to buy to achieve the portfolio’s target dollar duration then can be estimated by:

Approximate number of contracts ≈ [(D_T-D_I)P_I/(D_CTDP_CTD)]×Conversion factor for the CTD bond

where

D_T = target duration for the portfolio

D_I = initial duration for the portfolio

P_I = initial market value of the portfolio

D_CTD = the duration of the cheapest-to-deliver bond

P_CTD = the price of the cheapest-to-deliver bond

If the manager wishes to increase the duration, then D_T will be greater than D_I and the equation will have a positive sign. Thus, futures contracts will be purchased. The opposite is true if the objective is to shorten the portfolio duration. It should be kept in mind that the expression given is only an approximation.

Question 7

Comparison with Selection of Equity Managers

Answer 7

Selecting a fixed-income manager has both similarities with and differences from the selection of an equity manager.

1. In both cases, a consultant is frequently used to identify a universe of suitable manager candidates (because of the consultants’ large databases).
2. In both sectors, the available evidence indicates that past performance is not a reliable guide to future results.
3. The same qualitative factors are common to both analyses: philosophy of the manager and organization, market opportunity, competitive advantages, delegation of responsibility, experience of the professionals, and so on.
4. Management fees and expenses are vitally important in both areas, because they often reduce or eliminate the alpha that managers are able to earn gross of expenses. If anything, fees are more important in the fixed-income area, because fixed-income funds have a higher ratio of fees to expected outperformance.

Question 8

Credit Swaps

Answer 8

• Among all credit derivative products, the credit default swap is the most popular and is commonly recognized as the basic building block of the credit derivative market.
• 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. For short-dated credit, investors may pay this fee up front. In the case of a credit event, the protection seller compensates the buyer for the loss on the investment, and the settlement by the protection buyer can take the form of either physical delivery or a negotiated cash payment equivalent to the market value of the defaulted securities.
• Credit default swaps provide great flexibility to investors. In most cases, it is more efficient for investors to buy protection in the default swap market than selling or shorting assets. Because default swaps are negotiated over the counter, they can be tailored specifically toward investors’ needs.

Question 9

Hedging with Options

Answer 9

• There are two hedging strategies in which options are used to protect against a rise in interest rates: protective put buying and covered call writing. The protective put buying strategy establishes a minimum value for the portfolio but allows the manager to benefit from a decline in rates. The establishment of a floor for the portfolio is not without a cost. The performance of the portfolio will be reduced by the cost of the put option.
• The covered call writer, believing that the market will not trade much higher or much lower than its present level, sells out-of-the-money calls against an existing bond portfolio. The sale of the calls brings in premium income that provides partial protection in case rates increase.
• There is limited upside potential for the covered call writer. Covered call writing yields best results if prices are essentially going nowhere; the added income from the sale of options would then be obtained without sacrificing any gains.
• Interest rate **caps **— call options or series of call options on an interest rate to create a cap (or ceiling) for funding cost — and interest rate **floors **— put options or series of put options on an interest rate—can create a minimum earning rate. The combination of a cap and a floor creates a collar.
• Banks can use caps to effectively place a maximum interest rate on short-term borrowings; specifically, a bank will want the cap rate (the exercise interest rate for a cap) plus the cost of the cap to be less than its long-term lending rate.

Question 10

Currency Risk

Answer 10

The standard measure of the currency risk effect on foreign asset returns involves splitting the currency effect into:

1) the expected effect captured by the forward discount or forward premium (the forward rate less the spot rate, divided by the spot rate; called the forward discount if negative) and
2) the unexpected effect, defined as the unexpected movement of the foreign currency relative to its forward rate.

Question 11

Bond and Interest Rate Options

Answer 11

• Options can be written on cash instruments or futures. Several exchange-traded option contracts have underlying instruments that are debt instruments. These contracts are referred to as options on physicals. In general, however, options on futures have been far more popular than options on physicals. Market participants have made increasingly greater use of over-the-counter options on Treasury and mortgage-backed securities.
• An option on a futures contract, commonly referred to as a futures option, gives the buyer the right to buy from or sell to the writer a designated futures contract at the strike price at any time during the life of the option.
• The duration of an option can be calculated with the following formula:

Duration for an option = Delta of option × Duration of underlying instrument × (Price of underlying)/ (Price of option instrument)

• It also depends on the price responsiveness of the option to a change in the underlying instrument, as measured by the option’s delta.
• Because the delta of a call option is positive, the duration of a bond call option will be positive. Thus, when interest rates decline, the value of a bond call option will rise. A put option, however, has a delta that is negative. Thus, duration is negative. Consequently, when interest rates rise, the value of a put option rises.

Question 12

Historical Performance as a Predictor of Future Performance of Bond Managers

Answer 12

Over long periods of time (15 years or more) and when fund fees and expenses are factored in, the realized alpha of fixed-income managers has averaged very close to zero and little evidence of persistence exits. So it is clear that selecting a manager purely on the basis of historical performance is not a good approach to manager selection.

Question 13

Local currency correlations vs. their US dollar equivalent correlations,

Currency risk

Answer 13

• Overall, local currency correlations tend to be higher than their US dollar equivalent correlations. Such deviations are attributed to currency volatility, which tends to reduce the correlation among international bond indices when measured in US dollars.
• Currency risk—the risk associated with the uncertainty about the exchange rate at which proceeds in the foreign currency can be converted into the investor’s home currency.

Question 14

Hedging Currency Risk, Hedged Return (HR)

Answer 14

The three main methods of currency hedging are:

• forward hedging;
• proxy hedging; and
• cross hedging.

Forward hedging involves the use of a forward contract between the bond’s currency and the home currency. Proxy hedging involves using a forward contract between the home currency and a currency that is highly correlated with the bond’s currency. The investor may use proxy hedging because forward markets in the bond’s currency are relatively undeveloped, or because it is otherwise cheaper to hedge using a proxy.

In the context of currency hedging, cross hedging refers to hedging using two currencies other than the home currency and is a technique used to convert the currency risk of the bond into a different exposure that has less risk for the investor.

If IRP holds:

HR (hedged return) ≈ i_d + (r_f – i_f)

In other words, the hedged bond return can be viewed as the sum of the domestic risk-free interest rate (i_d) plus the bond’s local risk premium (its excess return in relation to the local risk-free rate) of the foreign bond.

r_f - foreign bond return in local currency terms

Question 15

Margin requirement as an advantage of using futures instead of cash instruments to alter portfolio risk?

Answer 15

Lower margin requirements are one of the advantages of using futures instead of cash market instruments. The margin requirements are lower for futures, which allows for greater leverage.

Question 16

Transfer of securities (with related costs) in Repo

Answer 16

Transfer agreements take a variety of forms:

1. Physical delivery of the securities. Although this arrangement is possible, the high cost associated with physical delivery may make this method unworkable, particularly for short-term transactions.
2. A common arrangement is for the securities to be processed by means of credits and debits to the accounts of banks acting as clearing agents for their customers (in the United States, these would be credit and debits to the banks’ Federal Reserve Bank accounts).
3. Another common arrangement is to deliver the securities to a custodial account at the seller’s bank. The bank takes possession of the securities and will see that both parties’ interests are served; in essence, the bank acts as a trustee for both parties. This arrangement reduces the costs because delivery charges are minimized and only some accounting entries are involved.
4. In some transactions, the buyer does not insist on delivery, particularly if the transaction is very short term (e.g., overnight), if the two parties have a long history of doing business together, and if the seller’s financial standing and ethical reputation are both excellent.

Question 17

The three major sources of duration hedging error are

Answer 17

The three major sources of duration hedging error are

• incorrect duration calculations,
• inaccurate projected basis values, and
• inaccurate yield beta estimates.

Question 18

Proxy hedge

Answer 18

There are two reasons a manager may want to use a proxy hedge strategy:

1. The manager may expect one currency to underperform relative to another currency,
2. It may be more costly, or not possible, to establish a hedge in the currency in which the investment has been made.

Question 19

Other Risk Measures

Answer 19

Alternative measures have been used because of the restrictive conditions of a normal distribution. These have focused on the quantification of the undesirable left hand side of the distribution—the probability of returns less than the mean return. However, each of these alternatives has its own deficiency.

1. Semivariance measures the dispersion of the return outcomes that are below the target return.
   * Deficiency*: Although theoretically superior to the variance as a way of measuring risk, semivariance is not widely used in bond portfolio management for several reasons:

• It is computationally challenging for large portfolios.
• To the extent that investment returns are symmetric, semivariance is proportional to variance and so contains no additional information. To the extent that returns may not be symmetric, return asymmetries are very difficult to forecast and may not be a good forecast of future risk anyway. Plus, because we estimate downside risk with only half the data, we lose statistical accuracy.

2. Shortfall risk (or risk of loss) refers to the probability of not achieving some specified return target. The focus is on that part of the distribution that represents the downside from the designated return level.
   * Deficiency*: Shortfall risk does not account for the magnitude of losses in money terms.
3. Value at risk (VAR) is an estimate of the loss (in money terms) that the portfolio manager expects to be exceeded with a given level of probability over a specified time period.
   * Deficiency*: VAR does not indicate the magnitude of the very worst possible outcomes.

Question 20

Return and duration of leveraged portfolio

Answer 20

R_p(portfolio rate of return) = r_F+ (B/E)×(r_F−k)

• E = Amount of equity
• B = Amount of borrowed funds
• k = Cost of borrowing
• r_F = Return on funds invested = RETURN ON EQUITY
• (RETURN ON BORROWED FUNDS = r_f-k)

Besides magnification of returns, the second major effect of leveraging a bond portfolio is on the duration of the investor’s equity in the portfolio. That duration is typically higher than the duration of an otherwise identical, but unleveraged, bond portfolio, given that the duration of liabilities is low relative to the duration of the assets they are financing.

D_E= (D_AA−D_LL)/E

• A and L represent the market value of assets and liabilities, respectively
• E - amount of equity invested (E = A-L)
• DE - duration of equity
• D_A - the duration of the assets (the bond portfolio)
• D_L the duration of the liabilities (borrowings)

Question 21

Dollar duration

Answer 21

In the course of managing a portfolio, the portfolio manager may want to replace one security in the portfolio with another security while keeping portfolio duration constant. To achieve this, the concept of dollar duration or the duration impact of a one dollar investment in a security can be used.

Dollar duration = D_i×V_i/100

where V_i = market value of the portfolio position if held; the price of one bond if not held.

Although duration is an effective tool for measuring and controlling interest rate sensitivity, it is important to remember that there are limitations to this measure. For example, the accuracy of the measure decreases as the magnitude of the amount of interest rate change increases.

Question 22

Interest Rate Swaps

Answer 22

• An interest rate swap is a contract between two parties (counterparties) to exchange periodic interest payments based on a specified dollar amount of principal (notional principal amount). The interest payments on the notional principal amount are calculated by multiplying the specified interest rate times the notional principal amount. These interest payments are the only amounts exchanged; the notional principal amount is only a reference value.
• The traditional swap has one party (fixed-rate payer) obligated to make periodic payments at a fixed rate in return for the counter party (floating-rate payer) agreeing to make periodic payments based on a benchmark floating rate.
• The dollar duration of an interest rate swap from the perspective of a floating-rate payer is just the difference between the dollar duration of the two bond positions that make up the swap:

Dollar duration of a swap = Dollar duration of a fixed-rate bond – Dollar duration of a floating-rate bond

The dollar duration of the fixed-rate bond chiefly determines the dollar duration of the swap because the dollar duration of a floating-rate bond is small.

The advantage of an interest rate swap is that it is, from a transaction costs standpoint, a more efficient vehicle for accomplishing an asset/liability objective.

Question 23

Bond Portfolio Variance

Answer 23

The variance of a portfolio is determined by the weight of each security in the portfolio, the variance of each security, and the covariance between each pair of securities.

Two major problems are associated with using the variance or standard deviation to measure bond portfolio risk:

1. The number of the estimated parameters increases dramatically as the number of the bonds considered increases.
2. Accurately estimating the variances and covariances is difficult. Because the characteristics of a bond change as time passes, the estimation based on the historical bond data may not be useful. Besides the time to maturity factor, some securities may have embedded options, such as calls, puts, sinking fund provisions, and prepayments. These features change the security characteristics dramatically over time and further limit the use of historical estimates.

Question 24

Active versus Passive Management in international fixed-income markets

Answer 24

As a first step, investors in international fixed-income markets need to select a position on the passive/active spectrum.

The active manager seeks to add value through one or more of the following means:

1. Bond market selection
2. Currency selection. This is the selection of the amount of currency risk retained for each currency, in effect, the currency hedging decision.
3. Duration management/yield curve management. Duration management strategies and positioning along the yield curve within a given market can enhance portfolio return.
4. Sector selection
5. Credit analysis of issuers
6. Investing in markets outside the benchmark

​The duration measure of a portfolio that includes domestic and foreign bonds must recognize the correlation between the movements in interest rates in the home country and each nondomestic market.

Country beta - a measure of the sensitivity of a specified variable (e.g., yield) to a change in the comparable variable in another country.

Question 25

Strategies with Interest Rate Futures

Answer 25

• The prices of an interest rate futures contract are negatively correlated with the change in interest rates. Therefore, buying a futures contract will increase a portfolio’s sensitivity to interest rates, and the portfolio’s duration will increase. On the other hand, selling a futures contract will lower a portfolio’s sensitivity to interest rates and the portfolio’s duration will decrease.
• 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 are clear advantages to using futures contracts. Furthermore, for duration reduction, shorting the contract (i.e., selling the contract) is very effective. In general, because of the depth of the futures market and low transaction costs, futures contracts represent a very efficient tool for timely duration management.

Question 26

Leverage in fixed-income strategies

Answer 26

• The whole purpose of using leverage is to magnify the portfolio’s rate of return.
• However, the interest rate sensitivity of the equity in the portfolio usually increases.
• The larger the amount of borrowed funds, the greater the variation in potential outcomes. In other words, the higher the leverage, the higher the risk.
• The greater the variability in the annual return on the invested funds, the greater the variation in potential outcomes (i.e., the higher the risk).

Question 27

Developing Criteria for the Selection a Bond Manager

Answer 27

The value of due diligence is found in the details; a fundamental analysis of the manager’s strategy must be conducted. Here are some of the factors that should be considered:

1. Style analysis: In large part, the active risk and return are determined by the extent to which the portfolio differs from the benchmark’s construction—particularly with regard to overweighting of sectors and duration differences. An analysis of the manager’s historical style may prove helpful in explaining how the types of biases and quality of the views reflected in the portfolio weighting have affected a portfolio’s overall performance.
2. Selection bets: If an active manager believes that she possesses superior credit or security analysis skills, she may frequently deviate from the weights in the normal portfolio. By forecasting changes in relative credit spreads and identifying undervalued securities, the manager may attempt to increase the active return of the portfolio. The manager’s skill in this approach may be measured by decomposing the portfolio’s returns.
3. The organization’s investment process
4. Correlation of alphas: Many managers exhibit similarities in their management of a portfolio. If multiple managers are to be used, obviously the plan sponsor will prefer low to high correlation among managers’ alphas to control portfolio risk.

Question 28

Interest Rate Futures

Answer 28

• A futures contract is an enforceable contract between a buyer (seller) and an established exchange or its clearinghouse in which the buyer (seller) agrees to take (make) delivery of something at a specified price at the end of a designated period of time. The “something” that can be bought or sold is called the underlying (as in underlying asset or underlying instrument). The price at which the parties agree to exchange the underlying in the future is called the** futures price**. The designated date at which the parties must transact is called the settlement date or delivery date.
• The delivery process for the Treasury bond futures contract makes the contract interesting. In the settlement month, the seller of a futures contract (the short) is required to deliver to the buyer (the long) $100,000 par value of a 6 percent, 30-year Treasury bond. No such bond exists, however, so the seller must choose from other acceptable deliverable bonds that the exchange has specified.
• To make delivery equitable to both parties, and to tie cash to futures prices, the CBOT has introduced conversion factors for determining the invoice price of each acceptable deliverable Treasury issue against the Treasury bond futures contract. The conversion factor is determined by the CBOT before a contract with a specific settlement date begins trading. The short must notify the long of the actual bond that will be delivered one day before the delivery date.
• In selecting the issue to be delivered, the short will select, from all the deliverable issues and bond issues auctioned during the contract life, the one that is least expensive. This issue is referred to as the** cheapest-to-deliver **(CTD). The CTD plays a key role in the pricing of this futures contract.
• In addition to the option of which acceptable Treasury issue to deliver, sometimes referred to as the quality option or swap option, the short position has two additional options granted under CBOT delivery guidelines. The short position is permitted to decide when in the delivery month actual delivery will take place—a feature called the** timing option**. The other option is the right of the short position to give notice of intent to deliver up to 8:00 p.m. Chicago time after the closing of the exchange (3:15 p.m. Chicago time) on the date when the futures settlement price has been fixed. This option is referred to as the wild card option. The quality option, the timing option, and the wild card option (referred to in sum as the delivery options) mean that the long position can never be sure which Treasury bond will be delivered or when it will be delivered.

Question 29

Credit Options

Answer 29

Unlike ordinary debt options that protect investors against interest rate risk, credit options are structured to offer protection against credit risk. 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.

1. Credit Options Written on an Underlying Asset: **Binary credit options **provide payoffs contingent on the occurrence of a specified negative credit event.

In the case of a binary credit option, the negative event triggering a specified payout to the option buyer is default of a designated reference entity. The payoff of a binary credit option can also be based on the credit rating of the underlying asset.

2. Credit Spread Options: Another type of credit option is a call option in which the payoff is based on the spread over a benchmark rate. The payoff function of a credit spread call option is as follows:
   * Payoff* = Max[(Spread at the option maturity − K)×Notional amount × Riskfactor, 0]

where K is the strike spread, and the risk factor is the value change of the security for a one basis point change in the credit spread.

Question 30

Default risk and factors that affect the repo rate

Answer 30

A variety of factors will affect the repo rate. Among them are:

1. Quality of the collateral. The higher the quality of the securities, the lower the repo rate will be.
2. Term of the repo. Typically, the longer the maturity, the higher the rate will be. The very short end of the yield curve typically is upward sloping, leading to higher yields being required on longer-term repos.
3. *Delivery requirement. *There is a trade-off between risk and return: The greater control the repo investor (lender) has over the collateral, the lower the return will be.
4. Availability of collateral. Occasionally, some securities may be in short supply and difficult to obtain. In order to acquire these securities, the buyer of the securities (i.e., the lender of funds) may be willing to accept a lower rate. The more difficult it is to obtain the securities, the lower the repo rate.
5. Prevailing interest rates in the economy. As interest rates in general increase, the rates on repo transactions will increase. In other words, the higher the federal funds rate, the higher the repo rate will be.
6. Seasonal factors. Although minor compared with the other factors, there is a seasonal effect on the repo rate because some institutions’ supply of (and demand for) funds is influenced by seasonal factors.

Question 31

Combination Strategies in Fixed Income markets

Answer 31

An active/passive combination allocates a core component of the portfolio to a passive strategy and the balance to an active component. The passive strategy would replicate an index or some sector of the market. In the active portion, the manager is free to pursue a return maximization strategy (at some given level of risk).

An active/immunization combination also consists of two component portfolios: The immunized portfolio provides an assured return over the planning horizon while the second portfolio uses an active high-return/high-risk strategy. The immunized portfolio is intended to provide an assured absolute return source. An example of an active immunization strategy is a surplus protection strategy for a fully funded pension plan in which the liabilities are immunized and the portion of assets equal to the surplus is actively managed.

Question 32

Breakeven Spread Analysis

Answer 32

• Breakeven spread analysis can be used to quantify the amount of spread widening required to diminish a foreign yield advantage. Breakeven spread analysis does not account for exchange rate risk, but the information it provides can be helpful in assessing the risk in seeking higher yields.
• Note that the breakeven spread widening analysis must be associated with an investment horizon and must be based on the higher of the two countries’ durations. The analysis ignores the impact of currency movements.
• !!! Only if you are not told which bond to use to perform the calculation you should use one with the greater duration !!!

Question 33

Properties of normal distribution

Answer 33

For a normal distribution, standard deviation has the property that

• plus and minus one standard deviation from the mean of the distribution covers 68 percent of the outcomes;
• plus and minus two standard deviations covers 95 percent of outcomes; and,
• plus and minus three standard deviations covers 99 percent of outcomes.

Question 34

Emerging Market Debt

Answer 34

Because of its low correlation with domestic debt portfolios, EMD offers favorable diversification properties to a fixed-income portfolio. EMD has played an important role in core-plus fixed-income portfolios. Core-plus is a label for fixed-income mandates that permit the portfolio manager to add instruments with relatively high return potential, such as EMD and high-yield debt, to core holdings of investment-grade debt.

Question 35

A bond in a foreign country trades at a yield disadvantage if….

Answer 35

A bond in a foreign country trades at a yield disadvantage if the forward discount/premium combined with the yield differential has a negative value. In other wordsm a disadvantage exists if:

(foreign bond yield - domestic bond yield) - (foreign risk-free rate - domestic risk-free rate) < 0

A symbolic representation would be:

(R_j-R_d)-(c_j-c_d)<0

The assumption is the difference in the risk-free ratem represented by c_j-c_d is an accurate measure of the forward premium or discount, which, in fact, must be the case for freely-traded currencies under covered interest rate parity.

Question 36

Bond equivalent yield (BEY) basis

Answer 36

In the US, most bonds are generally semi-annual coupon paying bonds, so we calculate the semi-annual yield and then calculate the bond-equivalent yield (annualized) by simply doubling the semi-annual yield. This is done when the bonds have semi-annual coupon payments.

However, not all bonds pay semi-annual coupon, especially there are many non-US bonds that pay coupon annually and hence will have the annual yield that is calculated by the compounding rules.

BEY of annual-pay bond = 2 x [(1+ yield on annual-pay bond)^0.5 -1]

Let’s take an example. Let say that an annual coupon paying bond has a yield of 6.5%. The bond-equivalent yield will be calculated as follows:

BEY = 2*(1.065^^0.5 – 1) = 6.398%

Note that BEY will always be lesser than the effective annual yield or the YTM of annual pay bond because BEY doesn’t consider the effect of compounding.

Question 37

Credit Forwards

Answer 37

Credit forwards are another form of credit derivatives. Their payoffs are based on bond values or credit spreads. There are a buyer and a seller for a credit forward contract. For the buyer of a credit forward contract, the payoff functions as follows:

Payoff = (Credit spread at the forward contract maturity −  Contracted credit spread) × Notional amount × Risk factor

The maximum the buyer can lose is limited to the payoff amount in the event that the credit spread becomes zero. In a credit spread option, by contrast, the maximum that the option buyer can lose is the option premium.