Financial Education

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

When choosing a benchmark index for a fixed income portfolio, the chosen benchmark should have characteristics that reflect those of the desired portfolio. Important factors to consider include market value risk, income risk and liability framework risk.

Market value risk is the reaction to changes in interest rates. Longer duration portfolios have more exposure to market value risk.

Income risk relates to how dependable is a portfolio’s income stream. This is a function of how long fixed payments can be assured. Shorter duration portfolios have more exposure to income risk.

Liability framework risk is a tiered approach that attempts to manage duration and other factors to the actual liabilities being managed.

Financial futures markets typically use one instrument to hedge a position. For example, a 10-year note future might be used to hedge a position in 10-year Treasury securities. However, such hedges can often be imperfect due to the structure of futures markets. A futures position can be satisfied by delivery of a wide range of bonds, and the cheapest to deliver (CTD) option may have qualities that differ significantly from the bond being hedged.

In the January/February 2008 Financial Analysts Journal, Lawrence Morgan addresses this issue and provides an example: in February 2007, the 10-year T-note was yielding 4.625%, but the CTD for the June 2007 10-year note futures was the 4.25% November 2013 note – a 7 year instrument.

Morgan examines whether combination hedges, made by combining two hedging instruments, would provide a better match. Leschhorn (2001) developed and tested an approach for the German bond market in which the weights of the two hedging instruments were determined by their yield differentials. Morgan notes that this approach can frequently result in unstable hedge ratios.

Morgan extends the analysis to combination hedges weighted by option-adjusted and non-option adjusted modified durations, and finds that in general option-adjusted modified duration weighted combination hedges performed best.

The general purpose of portfolio immunization is risk reduction. In some cases, however, earning an additional return can more than compensate for increased volatility.

For example, an investor may be able to immunize a portfolio to a 6.0% return, or to accept a 6.5% return with a 95% confidence interval of 50 basis points. In such a case, 19 times out of 20 the latter strategy would result in a greater return than the immunized portfolio, and the investor may be willing to accept the risk.

The minimum acceptable return would be determined by the required terminal value, plus a safety margin called the cushion spread. This strategy immunizes the lower bound of the confidence interval limit on realized returns.

Active management strategies seek to add value by earning a higher return than their benchmark index. In fixed income portfolios there are two primary approaches to active management:

Large Risk Factor Mismatches

This strategy takes deliberate and sometimes sizable mismatches on risk factors other than duration, including credit spreads, yield curve and sector exposure. The goal is to earn more than enough additional return to compensate for the higher transaction costs.

Full Blown Active Management

Full blown active approaches seek only return maximization. They will accept large mismatches on any risk factor, including duration, in order to add value relative to the index.

Portfolio immunization to a single investment horizon is appropriate only when there is one liability that must be met. More frequently, a stream of liabilities or required cash flows must be met, requiring a multiple liability immunization.

Immunizing a stream of liabilities requires funds to pay all liabilities even if there is a parallel shift in interest rates. Duration alone is not sufficient for immunization in this case. The components of total return must be separately available to immunize each liability.

In order to immunize multiple liability streams, the following conditions must be in place:

• Composite duration of assets matches composite duration of liabilities
• The distribution of asset durations must be wider than the distribution of liability durations