Source - Yield Curve Strategies - Robert W. Kopprasch
1. Active yield curve strategies are designed to capitalize on expectations regarding the level, slope or shape (curvature) of yield curves.
2. Helpful heuristic for understanding convexity is that, for zero-coupon bonds
a. Macaulay duration increase linearly with maturity - a 30-year zero-coupon bond has three times the duration of a 10-year zero-coupon bond
b. Convexity is approx proportional to duration squared; therefore a 30-year zero-coupon has about nine time the convexity of 10-year zero-coupon bond
c. Coupon-paying bonds have more convexity than zero-coupon bonds of the same duration - a 30-year coupon-paying bond with a duration of approximately 18 years has more convexity than an 18-year
- Although convexity can be a valuable tool when positioning a portfolio, it is important to remember that convexity is second-order effect; it operates behing duration in importance and can largely be ignored for small yield changes.
- Adding convexity is not free. Portfolios with higher convexity are most often characterized by lower yields.
- Portfolios with larger convexities often have lower yields. Investors will be willing to pay for increased convexity when they expect yields to change by more than enough to cover the sacrifice in yield.
- Convexity can be increased by selling MBS securities and buying would decrease convexity in a portfolio
- Convexity can be sold by selling a call on the bonds he owns or selling a put on bonds he would like to own. The option premium received would augment the yield of the portfolio. The selling lowers convexity in the portfolio, which is acceptable if he expects future volatility to be lower than that reflected in current option prices. Buying MBSs also provides an option-writing opportunity, in this case selling a prepayment option to homeowners.
Measures of Duration
- Money duration is a measure of the price change in units of the currecnt in which bond is denominated.
- PVBP is an estimate of the change in a bond's price given 1 bp change in yield to maturity. PVBP "scales" money duration so that it can be interpreted as money gained or lost for each basis point change in reference interest rate.
- Condor and employ four positions, much like a butterfly with an elongated body. Each pair of duration-neutral trades would result in a profit if the yield curve adds curvature. The trades at the short end of the curve (going long the 1-year bond and short the 3-year bond) would profit if that end of the curve gets steeper. In addition, the trades at the long end of the curve (going short the 10-year bond and long the long-term bond) would profit if that end of the curve becomes flatter.
Strategies
- If interest rates rise and the yield curve steepens as expected, then shortening the Fund’s duration from a neutral position to one that is shorter than the benchmark will improve the portfolio’s return relative to the benchmark. This duration management strategy will avoid losses from long-term interest rate increases.
- In a stable yield curve environment, holding bonds with higher convexity negatively affects portfolio performance. These bonds have lower yields than bonds with lower convexity, all else being equal. The 5-year US Treasury has higher convexity than the negative convexity 30-year MBS bond. So, by selling the 5-year Treasury and purchasing the 30-year MBS, will reduce the portfolio’s convexity and enhance its yield without violating the duration mandate versus the benchmark.
- Impact of buying short-dated options on Bond Futures vs. holding Bonds
Short maturity at- or near-the-money options on long-term bond futures contain a great deal of convexity. Thus, options increase the convexity of the client’s portfolio. Options are added in anticipation of a significant change in rates. If the yield curve remains stable, the portfolio will experience a loss from both the initial purchase price of the options and the foregone interest income on the liquidated bonds.
- Buying MBS vs. Buying option on Bond Futures when YC is expected to shift down
Purchasing a near-the-money call option on Treasury bond futures would add convexity and better position the portfolio for the forecasted downward parallel shift in the yield curve.
Buying an MBS would decrease convexity, which would not be ideal given expectation of a downward parallel shift in the yield curve.
In the case of an instantaneous downward parallel shift in the yield curve, a portfolio with added convexity resulting from the purchase of a near-the-money option on Treasury bond futures would increase in value more than a portfolio without the call option. Purchasing an MBS would decrease convexity, which would not be ideal given expectation of an instantaneous downward parallel shift in the yield curve.
There would be no significant effect on the portfolio resulting from duration because the durations are closely matched.
Analyzing expected excess returns against the expected magnitude of the credit-related risks is key to the bottom-up approach. Once the credit universe has been divided into sectors, the investor identifies the bonds with the best relative value within each sector. If Dynamo decides that two issuers have similar credit-related risks, then it will typically compare credit spread measures and buy the bonds of the issuer with the higher spread because those bonds likely have a higher potential for excess returns. For issuers with different credit-related risk, Dynamo must decide whether the additional spread adequately compensates for the additional credit risk.
Carry Trades
- Carry trades may or may not involve maturity mis-matches. Intra-market carry trades typically do involve different maturities, but inter-market carry trades frequently do not, especially if the currency is not hedged.
- Carry trades may involve only one yield curve, as is the case for intra-market trades. In addition, if two curves are involved they need not have different slopes provided there is a difference in the level of yields between markets.
- Inter-market carry trades do not, in general, break even if each yield curve goes to its forward rates. Intra-market trades will break even if the curve goes to the forward rates because, by construction of the forward rates, all points on the curve will earn the “first-period” rate (that is, the rate for the holding period being considered). Inter-market trades need not break even unless the “first-period” rate is the same in the two markets. If the currency exposure is not hedged, then breaking even also requires that there be no change in the currency exchange rate
- Inter-market trades should be assessed on the basis of returns hedged into a common currency. Doing so ensures that they are comparable. Neither local currency returns nor unhedged returns are comparable across markets because they involve different currency exposures/risks.
- The primary driver of inter-market trades is anticipated changes in yield differentials. Over horizons most relevant for active bond management, the capital gains/losses arising from yield movements generally dominate the income component of return (i.e., carry) and rolling down the curve. Hence, expectations with respect to yield movements are the primary driver of inter-market trade decisions.