Fixed Income Flashcards
IG bond more sensitive to interest rate changes
Investment-grade bonds have lower credit and default risks than high-yield bonds and are more sensitive to interest rate changes and credit migration, which cause credit spread volatility.
For investment-grade bonds, the risk of credit rating migration (credit deterioration)/ credit spread volatility, is greater than the risk of actual credit loss.
Credit loss is a primary consideration for high-yield bonds.
Agency MBS, CDO
If believe that market expectations of interest rate volatility will decrease, buy agency MBS.
If default correlations increase, the value of mezzanine (lower) tranches of CDO collateralised debt obligations usually increases relative to the value of senior tranches. Profit by selling the lower yielding (or selling short) senior class and buying the higher yielding lower class.
Whenever the value of a CDO is different from the value of its underlying collateral an arbitrage opportunity exists. In this example, the trade opportunity is to (1) short (alternatively, purchase credit default swaps on) the underlying bonds and (2) purchase the undervalued CDO.
collateral for a CDO consists of its underlying corporate bonds. Accordingly, there is no diversification benefit.
Calculating yield and bond price change with yield volatility
The expected change in yield based on a 99% confidence interval for the bond and a 1.50% yield volatility over 21 trading days equals 16 bps = (1.50% × 2.33 standard deviations × √21). We can quantify the bond’s market value change by multiplying the familiar (–ModDur × ∆Yield) expression by bond price to get $1,234,105 = ($75 million × 1.040175 ⨯ (–9.887 × .0016)).
Excess return for bond
Determining best value bond:
Excess return can be calculated ≈ (s)(t) – (Δs)(SD) – (t)(p)(L), where EXR = Excess return, s = Spread, t = Holding period, Δs = Change in spread, SD = Spread duration, p = Expected probability of default, and L = Expected loss severity.
instantaneous holding period return equals –EffSpreadDur × ∆Spread (as t=0)
if credit spreads remain stable, ∆Spread = 0, the expected excess spread is the simple difference between current OAS and expected loss
expected excess spread = (–(EffSpreadDur × ΔSpread)) less the product of LGD and POD
The data item most useful for relative value analysis is the expected probability of default.
Cashflow matching vs immunization
Cash flow matching entails building a dedicated portfolio of zero-coupon or fixed-income bonds to ensure there are sufficient cash inflows to pay the scheduled cash outflows. However, such a strategy is impractical and can lead to large cash flow holdings between payment dates, resulting in reinvestment risk and forgone returns on cash holdings. A cash flow matching strategy will mitigate the risk from non-parallel shifts in the yield curve.
Contingent immunization allows for active bond portfolio management until a minimum threshold in the surplus is reached.
A pure indexing approach for a broadly diversified bond index would be extremely costly because it requires purchasing all the constituent securities in the index. A more efficient and cost-effective way to track the index is an enhanced indexing strategy, whereby Serena would purchase fewer securities than the index but would match primary risk factors reflected in the index
Payer swaption vs writing receiver swaption
Hedge against rising interest rates: the potential losses on a payer swaption if rates fell would be limited to the option premium and would not be potentially large with uncertain timing, vs potential loss on writing a receiver swaption and entering into pay fixed swap if rates fell would be contingent on the interest rate and would be uncertain until termination of the contract.
laddered portfolio vs barbell
A laddered portfolio has lower convexity and dispersion than a barbell portfolio but more than a bullet portfolio, given comparable duration and cash flow yields, desirable aspects in liquidity management.
For definite barbell structure: subject to a greater degree of risk from yield curve twists and non-parallel shifts. For portfolio with highest level of convexity, which increases a portfolio’s structural risk.
OAS
Bond B is most likely callable because of the difference between its option-adjusted spread (OAS) and its Z-spread. The OAS considers the value of optionality in a bond’s cash flows. OAS is the constant spread that when added to all the one-period forward rates makes the arbitrage-free value of the bond equal to its market price. Z-spread is the yield spread that must be added to each point of the implied spot yield curve in order for the present value of the bond’s cash flows to equal its market price.
yield curve
When a wide spread curve flattens, the optimal portfolio construction strategy is to be underweight shorter-maturity bonds and overweight longer-maturity bonds.
Effective duration is used to measure the impact of a parallel change in the yield curve, not a steepening in the yield curve.
effects of a non-parallel shift in the yield curve can be reduced by minimizing the convexity of the bond portfolio.
Immunization
The two requirements to achieve immunization for multiple liabilities are for the money duration (or BPV) of the asset and liability to match and for the asset convexity to exceed the convexity of the liability. Yet, the convexity of the immunizing portfolio should be minimized in order to minimize dispersion and reduce structural risk.
Immunization is the process of structuring and managing a fixed-income portfolio to minimize the variance in the realized rate of return and to lock in the cash flow yield (internal rate of return) on the portfolio, not coupon rate, nor yield to maturity
Asset vs liability in yield changes
In a bear steepener, long rates rise faster than short rates in a non-parallel fashion. Given that the assets have lower convexity and dispersion than the liabilities, they will underperform; that is, the liabilities would change by a greater amount than the assets.
Credit risks, spread risks and model risks in bond deriviatives
most fixed-income derivatives contracts trade on credit risk–free government securities, and the pension plan’s assets consist of both investment-grade and speculative-grade corporate securities, making spread risk difficult to eliminate from the management of the portfolio.
Counterparty credit risk is essentially absent from exchange-traded derivatives, such as futures contracts, and can be essentially eliminated from over-the-counter derivatives, such as swaps, through inclusion of a Credit Support Annex. In contrast, model risk is implicit in the management of a defined-benefit pension plan, which is made up of Type IV liabilities (uncertain amount and uncertain timing).
number of futures contracts needed to fully remove the duration gap between the asset and liability portfolios
number of futures contracts needed to fully remove the duration gap between the asset and liability portfolios is given by Nf = (BPVL – BPVA)/BPVf.
the duration of assets is higher than the duration of liabilities so the pension fund will be hurt by rising interest rates and helped by falling interest rates.
Ruelas has under-hedged with a short position of less than 329 contracts, leaving the pension fund to be hurt by rising interest rates and helped by falling interest rates; therefore, he must believe interest rates will fall.
Rolling yield calculation
Rolling yield = Coupon income + Rolldown return. Coupon income is the sum of the bond’s annual current yield and interest on reinvestment income.
Coupon income = Annual average coupon payment/Current bond price
The rolldown return is equal to the bond’s percentage price change assuming an unchanged yield curve over the horizon period. The rolldown return = new bond price-old price/ old price
Total expected return on bonds
Total expected return =
Rolling yield (i.e. coupon yield + rolldown return
+/– E(Change in price based on investor’s benchmark yield view), i.e.(–MD × ∆Yield) + [½ × Convexity × (∆Yield)2]
+/– E(Change in price due to investor’s view of credit spread), i.e. (–MD × ∆Spread) + [½ × Convexity × (∆Spread)2]
+/– E(Currency gains or losses),
