Analysis of yield data.

Analysis of yield data

Yield curve usually tends to be upward sloping

Yields of various maturities and changes in these yields are highly correlated but this correlation decreases as the differences in maturity increases.

While there is a less similar dispersion around the mean yield change, for a longer bill, the price volatility is considerably greater than the longer term bills.

Bond Price movement and Duration

As interest rate goes up, the bond price decreases. A measure of volatility of bond prices is valuable. While a bond’s price maturity is a measure of interest rate sensitivity, it is not completely adequate since it only takes into account the final payment.

B = Sum ( Ct ( 1 + r ) ^–t )

The first derivative is dB / dr = - Sum ( Ct ( 1 + r ) ^{–t – 1} t )

Adjust this by B and ( 1 + r ) as

D = - Sum ( Ct( 1 + r ) ^–t / B) t

It gives bond’s effective maturity by weighting the payments by their proportion of the bon’s present value.

It correctly measures the bond’s interest rate sensitivity to local changes in interest rates.

dB / B = - D * ( dr / ( 1 + r ) )

Rules of duration

Duration of a zero coupon bond is time to maturity

Holding the maturity and yield constant, the longer time to maturity increases duration

Duration of level perpetuity is ( 1 + r ) / r

Modified duration

= - D / ( 1 + r )

Generalized duration

dP / P = - D2 * d( 1 + r1 ) / ( 1 + r1 )

Convexity

This measures the degree of inward curvature of the yield to price curve. It’s the second order term of the Taylor series expansion of the change in Price to change in interest rates.

Co = - Sum ( D ( t + 1 ) / 2 )

The change in price over price is

d P / P = - D *( dr / ( 1 + r ) ) + Co * ( dr / ( 1 + r ) ) ²

An application of duration

Immunization

Its adjustment of the portfolio so that the risk due to interest change is minimized. An example is duration matching, convexity matching, and asset matching.

Bond Investment strategies

Passive bond strategies

Laddered- each year, simply reinvest the proceeds from the maturity bond.

Barbell – Heavier investments made in the short and long maturities. The maturing bond and a portion of 16 year bond is sold and reinvested in 5 year and 20 year bonds.

Index – A particular bond index is selected as a benchmark and a bond portfolio is bought to mimic the bond index. Given bond indices typically have thousands of bonds and given the lower liquidity in the bond market, most bond index investors use a sampling approach to implement this strategy.

Active investment- Portfolio is constructed to outperform the benchmark by using an investment strategy based on manager’s expectations of market events.

Active bond strategies

Issue selection

Sector selection

Interest rate selection

Directional

Yield curve positioning

Types of yield curve shifts.

Parallel shift

Twists

Butterflies