BKFT 4010 - Managing Bond Portfolios

BKFT 4010 – Portfolio Management: Topic 5 - Managing Bond Portfolios

• Readings for Topic 5 come from BKM Investments, 11th Edition Book, Chapter 16, Sections 16.1, 16.2, 16.3, & 16.4.

Chapter Overview

• The chapter discusses interest rate risk and the interest rate sensitivity of bond prices.
• Duration, its determinants, and convexity are examined.
• Passive and active bond management strategies are explored.

Recap of Bond Basics

• Calculate the price of a 6% coupon bond with a face value of £100, yield to maturity of 9% and 2 years to maturity

Yield

• P represents the price of the bond.
• C represents the coupon, which is yearly
• F represents the face value of the bond.
• i represents the yield to maturity.
• n represents the years to maturity.
• For a bond with a 6% coupon rate, £100 face value, 9% yield to maturity, and 2 years to maturity, the price is calculated as follows: P = (£6 / (1 + 0.09)) + (£6 / (1 + 0.09)²) + (£100 / (1 + 0.09)²), resulting in P = £94.72
• Yield is the interest rate that equates the present value of cash flow payments received from a debt instrument with its value today.
• Coupon is not the same as yield.
• There is an inverse relationship between price and yield.

Risk Premium

• Bonds with the same maturity can have different yields.
• Risk premium is the spread between the yield of a risky bond and a default-free bond with the same maturity.
• Investors need to assess credit risk and liquidity risk to determine how much more interest they need to earn to hold a bond.

Credit Risk

• Credit risk or default risk refers to the risk that the issuer will be unable to make interest payments or pay back face value when the bond matures.
• U.S. Treasury bonds are almost default-free.
• Sovereign risk is exemplified by the situation between Germany and Greece during the Eurozone sovereign debt crisis.
• Credit rating agencies assess credit risk.
• Credit Default Swaps (CDS) are used to mitigate credit risk.

Liquidity Risk

• Liquidity is the ease and speed with which an asset can be turned into cash.
• U.S. Treasury bonds, German Bunds, and Japanese JGBs are the most liquid long-term bonds due to their widespread trading, quick selling ability, and low selling costs.
• Benchmark bonds such as 2Y, 5Y, and 10Y bonds are the most liquid.
• Credit risk and liquidity risk are often closely connected.

Yield Curves

• The term structure of interest rates is the yield curve.
• Bonds of the same issuer may have different yields depending on maturity.
• Positive (upward-sloping) yield curve, flat yield curve, negative/inverted (downward-sloping) yield curve are types of yield curves.

Demand for Bonds

• Demand for bonds, lower price and higher yield:
  • Lower relative expected return, for example, stock markets vs. bond markets
  • Higher inflation expectations lead to higher short-term interest rates
  • Higher central bank (short-term) interest rate, expectations theory
• Demand for bonds, higher price and lower yield:
  • Higher risk aversion: high-risk bonds sold and safe haven bonds bought
  • Liquidity concerns: in order to raise cash, bonds are sold
• Expected currency depreciation: future face value plus coupons lose value from the perspective of foreign investors
• Regulation: requirements that financial institutions hold a certain amount of government bonds
• Quantitative easing / yield curve control: deliberate intervention by central banks to influence long-term yields

Supply of bonds

• Supply of bonds involves a lower price with a higher yield
• Higher expected profitability of investment opportunities allows firms to be more willing in borrowing
• Higher inflation expectation allow for a fall in real cost of borrowing
• Increase in government deficit causes governments to issue more debt

Characteristics of Interest Rate Sensitivity

• Bond prices and yields are inversely related.
• An increase in a bond's yield to maturity results in a smaller price change than a decrease of equal magnitude.
• Long-term bonds tend to be more price sensitive than short-term bonds.
• As maturity increases, price sensitivity increases at a decreasing rate.
• Interest rate risk is inversely related to the bond's coupon rate.
• Price sensitivity is inversely related to the yield to maturity at which the bond is selling.

Duration

• Duration is a measure of the effective maturity of a bond.
• It is the weighted average of the times until each payment is received.
• The weights are proportional to the present value of the payment.
• Duration is equal to maturity for zero-coupon bonds.
• Duration is less than maturity for coupon bonds.
• Duration measures the average waiting time for all cash flows promised by a bond, discounted for the time value of money.
• It provides a close approximation of the effect of a change in yield on the bond's price.
• A 1% change in yield causes an approximate percentage change in price equal to the bond's duration.
• The need to adjust for the duration when buying 10Y US Treasury Bonds and selling 2Y US Treasury Bonds with $100,000 DV01 (“dollar value per 1 basis point").
• Without outright interest rate risk, the asset manager benefits from an inversion of the yield curve if the 10Y yield falls more (or rises less) than the 2Y yield.
• It is wrong to be indifferent whether the 2Y and 10Y yields rise or fall by the same magnitude, convexity needs to be monitored
• An asset manager will profit more when yields fall more than when yields rise.

Duration Calculation

• The formula for duration calculation is: D = Σ [t × wt] from t=1 to T, where wt = CFt / (1 + y) / P.
• CFt is the cash flow at time t, P is the price of the bond, and y is the yield to maturity.

Interest Rate Risk

• The duration-price relationship indicates the price change is proportional to duration.
• ΔP/P = -D × [Δ(1 + y) / (1 + y)], where D* = Modified duration.
• Modified duration formula: ΔP/P = -D*Δy.
• Two bonds may have equal duration but different coupon structures, like an 8% coupon bond and a zero-coupon bond maturing in the same period.
• Equal duration leads to the same interest rate sensitivity.

Duration Rules

• The duration of a zero-coupon bond equals its time to maturity.
• Holding maturity constant, a bond's duration is higher when the coupon rate is lower.
• Holding the coupon rate constant, a bond's duration generally increases with its time to maturity.
• Holding other factors constant, the duration of a coupon bond is higher when the bond's yield to maturity is lower
• The duration of a level perpetuity formula is (1 + y) / y

Convexity

• The relationship between bond prices and yields is not linear.
• The duration rule is a good approximation only for small changes in bond yields.
• Bonds with greater convexity have more curvature in the price-yield relationship.
• Convexity describes the asymmetrical price responses to changes in a bond's yield to maturity.
• The positive price impact of a yield decrease is greater than the negative price impact of the same yield increase.

Convexity Calculation

• Convexity formula: Convexity = (1/P) * Σ [C * t * (t+1) / (1 + YTM)^(t+2)] + [FV * n * (n+1) / (1 + YTM)^(n+2)]
• Adjustment the price using this equation: ΔP ≈ -Duration × ΔY + (1/2) × Convexity × (ΔY)² .
• Investors like convexity, as the bigger price increases when yields fall than losses when yields rise.
• The more volatile the interest rates, the more attractive this asymmetry is.
• Bonds with greater convexity have higher prices and/or lower yields, all else equal.
• Mortgage bonds offer negative convexity due to the embedded prepayment option that homeowners have in their mortgages.
• Prepayment option gives homeowners the ability to pay off their mortgages early, affecting the cash flows of the mortgage-backed bond.
• When interest rates fall, more homeowners are likely to refinance and pay off their mortgages earlier than expected.
• Callable bonds give the issuer the right to call the bond if interest rates drop, usually at a specified price
• In mortgage bonds, the bondholder faces prepayment risk due to homeowner refinance/sell decisions, an indirect callability form.

Passive Management

• Two passive bond portfolio strategies are indexing and immunization.
• Both see market prices as being correct.
• They differ greatly in terms of risk.

Passive Management: Indexing

• Bond Index Funds contains thousands of issues, many infrequently traded, also turnover more than stock indexes as the bonds mature, and they only old a representative sample of the bonds in the actual index

Passive Management: Immunization

• Immunization is used to control interest rate risk.
• Widely implemented by pension funds, insurance companies, and banks.
• The interest rate exposure of assets and liabilities are matched in the portfolio.
• The duration of assets and liabilities are matched, price risk and reinvestment rate risk exactly cancel out, Value of assets match liabilities whether rates rise/fall
• In bond immunization, the strategy involves matching the duration of the bond portfolio with the investor's time horizon.
• If an investor needs a lump sum in 5 years, create a portfolio of bonds with a 5 year duration, where any changes in interest rates that would not significantly affect the ability to meet the liability in 5 years.

Cash Flow Matching

• Cash flow matching is equivalent to automatic immunization and is a dedication strategy,
• Not widely used because of constraints associated with bond choices

Active Management

• Examples of derivatives instruments used in active management:
  • Over-the-counter: interest rate swaps, forward rate agreements, caps, floor and collars (options).
• Exchange-traded: bond futures, options on bond futures, and STIR (short-term interest rate) futures