Financial Education

International bond managers can seek excess return from a variety of sources:

1. Bond market selection - choosing the best country in which to invest
2. Currency selection - deciding whether to hedge or retain currency risk
3. Duration/yield curve management - getting the most favorable returns within the selected market
4. Sector selection - choosing among government, corporate, local currency or dollar-denominated bonds
5. Issuer credit analysis - being able to identify improvement or deterioration in advance of changes in rating
6. Benchmark mismatches - investing in markets that are not included in the benchmark index

Changes in interest rates affect both the reinvestment rate earned on portfolio income (directly) and the value of the portfolio (inversely.) An immunization strategy is designed to lock in total return over a specified time horizon by creating a portfolio in which the two total return factors exactly offset each other.

To immunize a portfolio over a single period, the portfolio must have duration equal to the investment horizon and an initial present value of cash flows equal to the present value of the future liability.

Since yield changes over time will result in duration changes other than those caused solely by the passage of time, it is necessary to periodically rebalance an immunized portfolio. This must be done only if the benefits outweigh the costs. Some transaction costs must be borne in order to avoid duration mismatch, but some duration mismatch is needed to avoid transaction costs.

Typically the rebalancing will restore the dollar duration equivalency to the time horizon. Dollar duration is the product of Duration X Portfolio Value X 0.01.

To rebalance the dollar duration requires three steps:

1. Calculate present dollar duration based on the prevailing yield curve and time to maturity
2. Calculate the rebalancing ratio by dividing the original dollar duration by the new dollar duration. This can be expressed as the percentage change for each position by subtracting one and converting the result into percentage terms.
3. The new market value of the portfolio multiplied by the percentage change is the amount of cash that will be needed for rebalancing.

There are three primary types of credit risk:

• Default risk is the chance the issuer will fail to meet its obligations
• Credit spread risk is the chance the spread between the risky bond and risk-free securities will vary after purchase
• Downgrade risk is the chance a rating agency will lower its rating on the issuer

These risks can be hedged using option contracts.

A binary credit option pays off only if a specified negative event occurs. These can be used to hedge default risk or downgrade risk.

Credit spread options pay off based on the spread over a benchmark rate. They can be used to hedge credit spread risk.

Using leverage magnifies the return in a portfolio. If a portfolio can earn 7% and can borrow funds at 5%, the additional 2% accrues to the fund investors. Instead of earning 7,000 on a 100,000 investment, the manager borrows an additional 100,000 and can earn 14,000, but must pay 5,000 in interest. The 9,000 remaining equates to a 9% return for the investors.

If the fund fails to earn the cost of borrowing, the leverage will work in the opposite direction as a drag on returns.

Given the liquidity of certain types of bonds, many managers seeking leverage make use of repurchase agreements (repos). These are agreements to sell a set of securities and to buy them back at a later agreed-upon date and price. The price difference is called the repo interest.

Repos offer the borrower lower rates (due to the liquid collateral) and the lender higher returns than Treasury bonds. Several factors contribute to the final repo rate that will be charged:

• Quality of collateral - higher quality bonds result in a lower repo rate
• Term of the repo - a longer term equates to a higher repo rate
• Delivery requirement - if the lender takes physical delivery of the collateral there is no default risk and the repo rate will be lower. Escrow accounts will reduce the rate to a lesser extent relative to no delivery.
• Availability of the collateral - if the bonds being offered as collateral are difficult to buy, the lender may accept a lower rate for the repo
• Prevailing interest rates - repos are generally tied to short-term interest rates
• Seasonal factors - certain market participants may have seasonal factors that affect their supply and demand for capital

The difference between the cash price of a bond and the futures price is called its basis. Basis risk is the chance that basis will change between unpredictably between the time the hedge is initiated and the time the hedge is lifted.

If the bond underlying the futures contract differs from the portfolio bond (a situation known as a cross hedge) the basis risk can be substantial. In essence the hedge substitutes basis risk for price risk.

The hedge ratio equals the factor exposure on the portfolio divided by the factor exposure on the hedging instrument.

If the factor is limited to interest rate exposure and one assumes a fixed yield spread between the bond being hedged and the cheapest-to-deliver (CTD) bond on the futures contract, the hedge ratio equals the product of the duration and price of the hedged bond, divided by the product of the duration and price of the CTD bond.

A total return analysis is a tool used to determine how a particular trade will affect the return in a portfolio. Given a specific interest rate forecast, the manager can determine how the transaction’s reaction will affect the return and risk of the overall portfolio.

Since any single interest rate forecast is subject to considerable error, most managers will not rely on one. Scenario analysis runs several total return analyses using a wide range of reasonable assumptions. Benefits of scenario analysis include:

• The ability to assess the distribution of possible returns
• The ability to reverse the calculation and find the range of interest rate movements that would result in the desired outcome
• The ability to evaluate components of total return
• Applicability to entire trading strategies rather than merely single trades

Enhanced index strategies attempt to add modest additional return while minimizing tracking risk relative to a benchmark index. In fixed income portfolios, the following factors are the primary contributors to tracking risk.

• Portfolio duration - exposure to parallel shifts in the yield curve
• Key rate duration - exposure to nonparallel shifts in the yield curve
• Sector and quality - the percentage of bonds in the portfolio with given credit ratings, yields or sector exposures
• Sector duration - exposure to changes in sector spreads
• Quality spread duration - exposure to changes in credit spreads
• Sector/coupon/maturity cell weights - a matrix design to put sets of securities into cells that largely replicate various qualities
• Issuer exposure - controls against issuer-specific event risks

In the May 2007 Review of Financial Studies, Duarte, Longstaff and Yu examine the risk/return characteristics of commonly used fixed-income arbitrage strategies. They find that the strategies that require high levels of modeling produce significant positive excess returns even after adjusting for risk, transaction costs and management fees.

Fixed income arbitrage strategies tend to exploit small differences between intrinsic value and market prices for securities. There has been some debate as to whether they are truly low risk arbitrage or whether the small positive returns most frequently earned are offset by infrequent but dramatic losses.

Of five strategies tested, the ones requiring the greatest intellectual capital - yield curve, mortgage and capital structure arbitrage - produced the highest excess returns after controlling for risk and costs. Swap spread arbitrage also produced positive risk adjusted returns.

Volatility arbitrage, or selling options on fixed income instruments and hedging the underlying asset exposure, produced positive excess returns but also had periods of significant losses.

Research has shown a negative correlation between interest rates and credit spreads that some find counterintuitive. In the Summer 2007 Journal of Fixed Income, Lin and Curtillet find that different risk components may have different relationships with the interest rate.

Lin and Curtillet find that whether spreads widen in response to an increase in the Fed target rate depends on the lagged response of the yield curve.

On a longer term basis, credit spreads are not determined by interest rates. Instead, they tend to widen in response to crises, significant financial events, and recessions.

Standard Deviation

• Assumes returns are normally distributed
• Allows for probability distributions (confidence intervals)
• Disadvantage is that returns are not normally distributed, particularly when the bonds have embedded options

Semivariance

• Measures the dispersion of outcomes below the target rate of return
• Theoretically superior to variance or standard deviation because most investors are concerned primarily about risk to the downside
• Disadvantages:
  • Computationally challenging for large portfolios
  • If returns are symmetrical, it contains no additional information
  • If returns are not symmetrical, the return asymmetries are difficult to forecast
  • Use of only half the data reduces statistical accuracy

Shortfall risk

• Relates to probability of failing to achieve the specified target
• Disadvantage is that it does not account for the magnitude (in money terms) of losses

Value at Risk (VAR)

• Estimates loss (in money terms) portfolio is likely to encounter over a specified time at a given level of probability
• Disadvantage is that it does not indicate the magnitude of worst-case scenarios