Fixed Income Flashcards
(46 cards)
Discuss roles of fixed-income securities in portfolios and how fixed-income mandates may be classified.
Fixed income as an asset class provides 3-major roles when added to an investment portfolio:
diversification
regular cash flows
inflation protection (floating-rate securities and inflation-linked securities)
There are 2-major classifications of mandates:
liability-based mandates: which invest to fund future liabilities; and
total return mandates:which invest to track or beat a benchmark.
What are the types of liability-based mandates for fixed-income securities?
Cash-flow matching: funds liabilities with coupon and par amounts received on the dates the liabilities are paid.
Duration matching: matches asset and liability duration to achieve comparable results. Duration matching generally gives more flexibility in asset selection and, therefore, may meet the objective at a lower cost.
Contingent immunization: is a hybrid of active management with potential immunization. The portfolio must initially be overfunded and can be actively managed. If successful (unsuccessful), the surplus will grow (be lost) and the ultimate cost will end up being lower (higher) than from immunization.
What are the types of total return mandates for fixed-income securities?
Pure indexing: which exactly matches the holdings of the index.
Enhanced indexing: which allows modest deviations (but matches duration to control interest rate risk).
Active management: which does not restrict deviations versus the index and allows duration mismatches.
Describe fixed-income portfolio measures of risk and return as well as correlation characteristics.
To aggregate duration and convexity measures for a portfolio of fixed-income assets, the cash-weighted average of the durations and convexities of the individual bonds is usually used.
Duration times spread (DTS) = spread duration × credit spread. It reflects the fact that bonds with larger spreads tend to have larger movements in spread.
A manager who expects interest rates to rise (fall) will lower (increase) duration.
A manager who expects credit spreads to widen (narrow) will lower (increase) spread duration.
Relative value analysis involves the ranking of individual bonds according to fundamental value drivers in order to pick the best securities to express a top-down view on markets.
Describe bond market liquidity, including the differences among market sub-sectors, and discuss the effect of liquidity on fixed-income portfolio management.
Liquidity in the bond market (ability to buy or sell on a timely basis at or near fair market value) is substantially lower than in equity markets.
Most bonds do not trade or trade infrequently after issuance (said to go “off-the-run”).
The sheer number and variety of individual bond issues is immense.
The market is mostly over-the-counter with trade price and volume not reported.
Liquidity is highest for sovereign government, higher-quality, and most recently issued (on-the-run) bonds.
Smaller issues are generally less liquid.
Why are smaller issue bonds generally less liquid?
Bond pricing data are more difficult to obtain.
Portfolio managers have to choose between more-liquid bonds or less-liquid bonds that may offer a liquidity premium.
Derivatives and ETFs are generally more liquid and are an alternative to direct investment in bonds.
Describe and interpret a model for fixed-income returns.
Return can be projected (or actual return decomposed) as the sum of the following:
1. Coupon income: annual coupon amount / current bond price.
2. Rolldown return, assuming no change in yield curve: (projected ending bond price [BP] − beginning BP) / beginning BP.
3. Price change due to investor yield change predictions: (–MD × ΔY) + (½ C × ΔY^2).
4. Price change due to investor yield change predictions: (–MD × ΔS) + (½ C × ΔS^2).
5. Currency G/L: projected change in value of foreign currencies weighted for exposure to the currency.
Rolling yield = Coupon income + rolldown return
Discuss the use of leverage, alternative methods for leveraging, and risks that leverage creates in fixed-income portfolios.
Leveraged portfolio return can be calculated as rI + [(VB / VE) × (rI − rB)].
If rI exceeds (is below) rB, the leverage enhances (reduces) portfolio return.
Repurchase agreements (and securities lending), futures contracts, and swaps can all be used to leverage return.
In addition to the detrimental effects if rI is less than rB, the lender of the funds can demand repayment, forcing liquidation of portfolio assets at fire sale prices, which can feed a financial crisis.
Discuss differences in managing fixed-income portfolios for taxable and tax-exempt investors.
Taxes complicate portfolio management, as managers seeking to maximize return must consider the different tax effects of each portfolio decision.
What is Macaulay duration?
Macaulay duration is the weighted average time to receive cash flows.
Macaulay duration increases linearly with maturity.
What is Modified duration?
Modified duration is the estimated percentage change in a bond price given a 1% change in yield [measured as Macaulay duration / (1 + the periodic yield of the bond)].
What is Effective duration?
Effective duration is the modeled estimated percentage change in a bond price given a 1% change in a benchmark curve. It is used for bonds with embedded options.
What is Key rate duration?
Key rate duration (partial duration) is the estimated percentage change in a bond price given a 1% change in a key benchmark maturity yield while other yields remain the same.
What is Empirical duration?
Empirical duration is the actual sensitivity of a bond’s price relative to movements in a benchmark rate from a linear regression.
What is Money duration?
Money duration (dollar duration) equals modified duration × market value. It gives a sense of size, as well as sensitivity.
What is the Price value of a basis point?
Price value of a basis point [DV01 or basis point value (BPV)] equals money duration × 0.0001. It measures the absolute currency sensitivity to a basis point move in rates.
What is Convexity?
Convexity measures the curvature of the relationship of price and yield. More-convex bonds are expected to outperform less-convex bonds when yields shift.
Convexity is approximately proportional to duration squared.
Convexity is also directly related to the dispersion of cash flows in time around the Macaulay duration.
What is Effective convexity?
Effective convexity models convexity when cash flows are not certain. It is used for bonds with embedded options.
What is Spread duration?
Spread duration is the sensitivity of a bond’s price to a unit change in spreads.
Describe liability-driven investing.
Liability-driven investing is a form of asset-liability management (ALM) that manages the assets in relation to the characteristics of the liabilities. This is easier when the future liability payouts are known in amount and timing. The liabilities are essentially the benchmark for making decisions.
Asset-driven investing is a less common form of ALM and adjusts the liabilities in relation to the characteristics of the assets.
Evaluate strategies for managing a single liability.
Immunization can be used to fund liabilities with a high degree of certainty. The assets are dedicated to this purpose and all cash flows are reinvested until needed for payout.
Cash flow matching is without risk, assuming there are no defaults. Bonds are bought and held in sufficient amount and pay date to meet the liabilities. It is the most restrictive strategy, and so typically costs more (has lowest return).
Duration matching achieves similar results, but is less restrictive in the assets selected. Matching Macaulay duration of the assets to liabilities balances the exposure between price and reinvestment risk. Duration and other portfolio statistics should be based on portfolio yield (IRR).
To immunize a single-period liability:
Initial PVA equals (or exceeds) PVL. (There are exceptions to this for more complex situations where initial portfolio IRR differs from initial discount rate of the liability.)
Match Macaulay durations (DA = DL).
Minimize portfolio convexity.
Rebalance the portfolio to maintain the duration match.
Immunization (duration matching) issues include the following:
The assets have greater convexity than the single date liability; therefore, the portfolio benefits from large parallel shifts but is at risk from curve twists (nonparallel shifts). Minimizing convexity minimizes this structural risk.
Immunization can be interpreted as zero replication, meaning a successful immunization will replicate the price and yield path of a zero-coupon bond that could have been used for a perfect cash flow match immunization.
Compare strategies for a single liability and for multiple liabilities, including alternative means of implementation.
Multiple liabilities can be cash flow matched with a portfolio of zero-coupon bonds or coupon-bearing bonds whose cash flows (P&I) most closely match the liability payouts. Duration matching can be done by matching the BPV of the assets and liabilities.
The rules are as follows:
Initial PVA equals (or exceeds) PVL (see the caveat given under single liability rules).
BPVA = BPVL
Asset dispersion of cash flows and convexity exceed those of the liabilities (but not by too much, in order to minimize structural risk exposure to curve reshaping).
Regularly rebalance the portfolio to maintain the BPV match.
Derivatives are often used to adjust the BPV of the assets and hedge or partially hedge the duration gap:
Buying (selling) futures or receive (pay) fixed swaps increases (decreases) asset duration and BPV.
Futures BPV ≈ BPVCTD / CFCTD
BPV = MD × V × 0.0001
Nf = (BPV of liability − BPV of current portfolio) / BPV of futures.
NP for swap = (BPV of liability − BPV of current portfolio) / BPV of 1 NP for the swap.
BPVswap is the difference in BPV between the fixed and floating sides.
Contingent immunization (CI) requires the portfolio be overfunded with a positive surplus (PVA > PVL). If the surplus is positive, the portfolio can be actively managed (not immunized):
If active management is successful, the return will exceed the initially available immunization rate, the surplus will grow, and the ultimate cost of the strategy will be less than immunizing.
If active management fails, the surplus will decline to zero and the portfolio must be immunized. The ultimate cost will exceed that of immunizing.
Describe construction, benefits, limitations, and risk–return characteristics of a laddered bond portfolio.
Laddered portfolios:
Can be useful in cash flow matching multiple liabilities.
Provide diversification across the yield curve and natural liquidity as a portion of the bonds come due each year. In an upward-sloping yield curve, this can also be desirable as each maturing bond is rolled over into the longest (and highest yielding) maturity used in the ladder.
Have more convexity than a bullet portfolio because their cash flows are more distributed.
Could be constructed with a sequence of target-date ETFs as an alternative to individual bonds.
Evaluate liability-based strategies under various interest rate scenarios and select a strategy to achieve a portfolio’s objectives.
A 100% hedge eliminates the duration gap (matches BPV of assets and liabilities).
In the normal scenario of BPVA < BPVL, a manager who expects interest rates to:
Increase will reduce the hedge size, leaving the BPV of assets less than that of a fully hedged duration gap. Leaving the BPV of assets at a lower level means they will decline in value less as interest rates increase.
Decrease will increase the hedge size, increasing the BPV of assets above that of a fully hedged duration gap. Increasing the BPV of assets means they will increase in value more as interest rates decrease.
Regarding the three swap methods of reducing a negative duration gap (increase BPV of assets):
Entering a receive-fixed swap is generally optimal if interest rates in the future are below the swap’s SFR.
Using a zero-cost collar (buy receiver swaption and sell payer swaption) is generally optimal if interest rates in the future are moderately higher (i.e., between the swap and payer swaption SFRs).
Buying a receiver swaption is generally optimal if interest rates in the future exceed the payer swaption SFR by some amount.
