Define yield to maturity (5)

- YTM is defined as the interest rate that makes the present value of the bonds payments equal to its price.
- To calculate, solve the bond price equation for the interest rate given the bonds price
- Internal rate of return, holding period return
- Assumes all coupons are reinvested at the yield
- YTM is NOT the same as current yield

Define current yield

Current yield is the bonds annual coupon payment divided by the bond price

Coupon rate (define)

Coupon rate divides the coupon payments by the par value

Yield to maturity vs holding period return

When the yield to maturity is unchanged over the holding period the rate of return will equal that yield.

When yields fluctuate, so too will the HPR.

YTM depends on the bond’s coupon, CURRENT price, and par value at maturity, which are all observable today.

HPR depends on the market price of the bond at the end of the holding period, which is not known today.

Determinants of bond safety (5)

- Coverage ratios (times interest earned, fixed charge coverage)
- Leverage ratio: debt to equity
- Liquidity ratio: current ratio (CA/CL), quick ratio (CA excl inventories/CL)
- Profitability ratios: indicators of firms overall financial health. ROA, ROE
- Cashflow to debt ratio: ratio of total cashflow to outstanding debt

Edward Altman test to discriminate bankruptcy

Assign a score based on financial characteristics. If score exceeds cutoff value firm deemed creditworthy. If below, significant bankruptcy risk in near future.

Pure yield curve

Curve for stripped (zero coupon) bond

On the run yield curve

Plot of yield as a function of maturity for recently issued coupon bonds selling at or near par value

Spot rate

Yield to maturity on zero coupon bonds ie the rate that prevails today for a time period corresponding to the zero’s maturity

Short rate

Interest rate for a given time interval, at different points in time

Forward interest rate

- Forward rates are interest rates that relate to forward maturities.
- Can be implied from the present yield curve
- Future interest rates are unknown. Therefore it is a FORWARD INTEREST RATE not a future short rate because it need not be the interest rate that actually will prevail at the future date.
- Forward rate can be thought of as comprised of expectations plus a liquidity premium. Forward rate should exceed the expected short rate

Theories of term structure (2)

- Expectations hypothesis

Forward rate equals market consensus expectations of the future short rate and liquidity premiums are zero - Liquidity preference

Investors require a premium to hold bonds with maturities different to their investment horizons. Theory is that short term investors dominate the market so the forward rate will generally exceed the expected short rate.

Does the yield curve reflect expectations of future rates

Yes, but it also reflects things such as liquidity premiums

Also forecasts of interest rates may have different investment considerations. (Are those changes driven by expected inflation rate or the real rate)

Define default premium(2)

Define risk structure of interest rates

- Compensation for the possibility of default.
- The difference between the corporate yield and govt bond yield

Risk structure of interest rates is the pattern of default premiums

Define credit default swaps

- Insurance policy on the default risk of a corporate bond or loan
- 5% means buyer pays seller $1.50 for each $1 of bond principal in the event of default
- Compensation can be physical (ie delivery of defaulted bond) or cash settled (issuer pays holder the difference between the par value of the bond and its market price)
- Pricing should reflect the difference in credit spread between the bond rating and the rating of the CDS issuer

Interest rate risk, list 4 properties

- Bond prices and yields are inversely related
- The price and yield relationship is nonlinear (convex)
- Long maturity bonds are more interest rate sensitive
- Lower coupon paying bonds are more interest rate sensitive

Also, sensitivity of a bond’s price to a change in yield is inversely related to the YTM at which the bond is currently selling

Applications for duration (2)

- Estimating the impact of interest rate changes

2. Positioning a portfolio to maximize the benefit from a correct view in interest rates

What determines duration (5)

- Duration of zero coupon bond equals its time to maturity
- Holding maturity constant, a bond’s duration is lower when the coupon rate is higher
- Holding coupon rate constant, duration generally increase with time to maturity. Duration always increases for bonds selling at par or at a premium. Note is trading at a deep discount, value of bond may be less price sensitive
- Duration of a coupon bond is higher when the YTM is lower
- Duration of a perpetuity = (1+y)/y. Note with perpetuity the earlier PV weighted flows dominate the computation of duration

Portfolio immunization steps (4)

- Calculate the duration of the liability
- Calculate the duration of the asset portfolio
- Find the asset mix that sets the duration of assets equal to the 7 year duration of the liabilities
- Fully fund the obligation

Modified duration represents

MD represents the price sensitivity of a bond for a 100bp change in yield

Define duration

Duration: the weighted average lengths of time prior to cashflows, the weights being the present values of the corresponding payments

Duration of a bond is the maturity of a zero coupon bond with equal price sensitivity

Define dollar duration

Dollar duration of a bond equals the actual dollar change in the value of the bond due to a small change in yield

Dollar durations are additive, can deliver the total market value movement of a portfolio by summing the dollar durations

Price value of a basis point

Price value if a basis point is the change in the price of a bond for a change in yield of 1bp

Dumbbell bullet analysis

Dumbbell: combination or a portfolio of 2 bods where the holdings of the 2 bonds are determined to satisfy certain criteria

Select bonds such that the combination equals the value of a third bond, the bullet

Convexity

Curvature of the price yield relationship

Rate of change of the slope of the price yield curve

Convexity is desirable because bonds with greater curvature gain more in price as yields fall and lose less when yields rise.

Name and describe 2 types of passive bond management

- Attempt to replicate performance of a given bond index. Will have the same risk-reward profile as the index
- Immunization techniques, ie shield overall financial status of the institution from exposure to interest rate fluctuations. Zero risk profile in which interest rate movements have no impact on the value of the firm.

Problems with replicating a bond benchmark (4)

- Indexes generally have thousand of securities and can be thinly traded
- Securities included in indices constantly change. (New ones added, others dropped when within 1 yr to maturity)
- Interest income is earned and must be reinvested
- Usually use sampling techniques to replicate

Two types of interest rate risk

- Price risk

2. Reinvestment rate risk

Dedication strategy

- Dedication strategy is the cashflow matching on a multi period basis.
- Cash flow matching automatically immunizes the portfolio from interest rate movement because the cash flow from the obligation and the bond exactly offset each other.
- Once the cashflows are matched there is no need for rebalancing
- Cashflow matching is not always possible. Eg, may need maturities that do not exist in the bond markets (pension funds require longer bonds). Firm may also seek to add value

Immunization, problems with

- If the yield curve is not flat, must adjust such that the definition of duration is modified, may need to discount each CF by that CFs spot rather than the overall bond yield
- Immunization is essentially a NOMINAL notion and makes sense only for nominal liabilities

Outperformance of an active bond portfolio can be categorized according to different bond “swaps”.

- Substitute swap (driven by mispriced securities)
- Inter market spread (driven by opinion of impending change in sector yield spreads)
- Rate anticipation swap (driven by opinion on the direction of interest rates)
- Pure yield pick up swap (increasing YTM of portfolio)
- Tax swap (driven by managing assess able tax on a portfolio.

2 sources of potential value in active bond manager t

- Interest rate forecasting

2. Identification of relative mispricing within the fixed income market

Current yield: define, what is weakness

Current yield is the annual coupon payment divided by the bond price.

Weakness: current yield does not account for capital gain/loss for a bond not trading at par.

Yield to maturity, define, what is the weakness?

Yield to maturity is the internal rate of return on an investment in the bond. It is the compound rate of return over the life of the bond.

Weakness: YTM assumes that coupons are reinvested at that yield (yields may change)

Define realized compound yield, what is the weakness

Realized compound yield takes into consideration the actual reinvestment rates.

Weakness, the realized compound yield can be found after the period has elapsed, it cannot be computed in advance without a forecast of future reinvestment rates. Affected by forecast of reinvestment rates, holding period and yield of the bond at the end of the investors holding period.

Forward rate can be viewed as:

Sum of the markets expectation of the future short rate plus a potential risk or liquidity premium.

Expectations theory: liquidity premium is zero, therefore market’s expectations of short rates can define the yield curve. No risk premia is built into bond prices

Liquidity preference theory: liquidity premium is positive, therefore forward rate is more than the market’s expectation of future short rates. Predicated on the assumption that financial markets are dominated by short term investors who demand a premium to hold longer maturity investments.

Why would a callable bond have a higher yield

Because it needs to compensate the bond holder for the potential risk of missing out on capital gain should interest rates fall and the bond is recalled.

If asked a question about whether various types of FI instruments have a higher yield than govt bond, be careful of FRNs and inverse FRNs. Due to?

FRNS and inverse FRNS, whether they are higher than govt bond yields will depend on the shape of the yield curve and inflation expectations.

Difference between current yield and yield to maturity

Current yield is only the cashflow part of the return, whereas YTM incorporates capital gains and losses.

YTM can therefore represent the total implied return from between the value of the bond and the future cashflows.

Predictions for interest rates, eg between 1 yr and 2 yr, what rates are important

Important rate: the 1 year rate in 1 year’s time

Expectations for inflation and the real rate

Expectations for the future impact the shape of the curve

Flat curve: what are curve expectations?

A flat curve does not meant he market expects flat rates. Should mean market expects rates to go down.

For bonds selling at a discount, what yield measure is higher

YTM > current yield > coupon rate

Which ratios are used by bond ratings agencies to compare a company’s earnings to fixed costs

Coverage ratios are used to compare a company’s earnings to fixed costs