Financial Education

For individuals drawing on retirement funds, a 4% withdrawal rate is generally recommended to result in only a small chance of the portfolio running out of money. In the October 2007 Journal of Financial Planning Spitzer, Strieter and Singh simulate thousands of 30-year periods to assess the overall probability of running out of funds.

They find that a standard 50/50 split between stocks and bonds can allow for a 4.4% withdrawal rate with just a 10% chance of depleting funds. Withdrawal rates of up to 6% can be supported with stock allocations of 75% or more.

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

Secondary markets are those in which securities that have already been issued trade. Transactions occur between investors, and the proceeds do not affect the issuer. Instead, one investor gives another investor cash in exchange for the securities.

Secondary markets provide liquidity to the investors who initially buy the securities. Investors value liquidity because changes in their circumstances may require them to sell the security in order to use the cash for other purposes. By having a liquid secondary market, investors are willing to pay more (accept a lower return) when buying primary issues. This helps issuers raise money at more favorable rates.

Secondary markets also offer issuers price discovery – new issues can be priced according to the value of other similar securities.

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

The primary market refers to trading in new issues of securities. This could be bond issues by corporations or governments, stock issues by corporations or other types of securities in which the initial trade is being made by transferring funds from investors to the security issuer.

Consider, for example, the initial public offering of a stock. The company sells shares to investors, increasing the total number of shares outstanding. Proceeds from the sale increase the company’s cash position, which enables it to invest in new opportunities.

Compared to cash markets, futures offer a number of advantages for controlling duration in a fixed income portfolio. These include:

• Cost effectiveness
• Liquidity
• Deep markets
• Ability to shorten duration by shorting futures contracts

To alter the duration of a portfolio using futures contracts it is necessary to know how many contracts to buy or sell.

Target duration = Current dollar duration + Dollar duration of the futures contracts

Dollar duration of the futures contracts = Dollar duration per contract X the number of contracts

The number of contracts = the difference between the target duration and the initial duration, multiplied by the portfolio value, all divided by the dollar duration per futures contract.

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.