Reading 9 Flashcards
Fixed income
Buy and hold versus laddered
Buy and hold: no sales or trading are planned
Laddered: somewhat equal amount of par comes due periodically
Inflation-linked versus floating rate bonds
Inflation linked: par (even for calculation) is adjusted for inflation, coupon rate remains the same. Coupon amount increases as a result
Floating rate bonds: coupon is usually MRR + 100 bps. No adjustment is made to the par amount. Thus, coupons are inflation protected, but not the principal.
which one is better - inflation linked or floating coupon?
depends
Fixed Income Liability Based Mandates
portfolio assets that are managed solely to meet expected future liability payouts. all asset cash flows are reinvested until paid out to meet the liabilities. Often called immunization.
Duration matching
matches duration of the assets and liabilities so the two will fluctuate in a similar way as interest rate changes, such that their ending values will remain matched
Contingent Immunization (CI)
hybrid of active management and immunization. Portfolio is initially funded with more money that required to meet the future liability payouts.
PVA exceeds PVL, difference is surplus
As long as surplus is positive, the portfolio can be managed in any way the manager believes will add value.
If CI succeeds, the surplus will grow and the ultimate cost of CI will be less than that of initially immunizing.
If active management is unsuccessful, and the surplus declines to zero, the portfolio much be immediately immunized and the ultimate cost of CI will be more than that of initial immunization, but by a known amount
Total Return Mandates
Do not seek to fund future liabilities, but may target an absolute rate of return or seek to equal or outperform (relative return versus) a benchmark.
The key metrics to evaluate such portfolios are active return (portfolio return less return of the relevant benchmark, also called value added or alpha) and volatility of that active return (standard deviation of active return, also called active risk, tracking error or tracking risk). includes:
- pure indexing: replicate bond index returns, active return and risk = 0
- enhanced indexing: allows some additional flexibility in constructing the portfolio and seeks to add some modest active return. typically, duration is still matched to the index, but some risk mismatches such as modest over or underweighting of sectors and quality are allows.
- active management: allows much larger deviations from the risk factors of the index and seeks greater active returns, durations can also be mismatched and portfolio turnover can be much higher,
How are durations linked to leverage?
Borrowing is normally done at shorter-term interest rates and those costs can increase faster than return on assets if interest rates increase.
Asset duration normally exceeds the liability duration in a leveraged portfolio.
Leveraged Portfolio’s return formula
portfolio return (amount) / portfolio equity
leveraged portfolio: return on invested assets formula
(amount of leverage/ amount of equity invested) x (return on invested assets - rate paid on borrowings)
Repurchase Agreements (repos)
A securities owner “Sells” a security for cash and simultaneously agrees to buy it back at a specific future date. The repo is functionally a way to borrow money and the assets are the collateral for the loan.
The actual securities “sold” are not typically specified
Macaulay Duration
Weighted average time to receive the cash flows, where weights are the PV of cash flows
Higher Macaulay duration means investors are waiting longer to receive cash flows and hence face higher price volatility when yields change
Modified duration
Macaulay duration divided by (1+ bond yield)
This gives the approximate expected % change in bond price for a 1% change in yield. eg a bond with a modified duration of 7 is expected to fall by approximately 7% when yields rise by 1%
Effective duration
sensitivity of a bond’s price to a PARALLEL shift change in a benchmark yield curve, based on directly modeling changes in prices due to changes in a benchmark curve
This gives the approximate expected % change in bond price for a 1% change in benchmark curve. Effective duration is used for complex bonds where cash flows are not certain, such as bonds with embedded options
Convexity
Convexity is valuable to bondholders when yields are expected to change. This is because positive convexity, as just described, implies that a bond price is expected to rise by more than that implied by duration alone when yields fall and fall by less than that implied by duration alone when yields rise. Note that this will mean investors will pay higher prices for higher convexity bonds (and accept lower yields vs. yields of other less convex bonds).
Why is convexity a second order measure?
meaning that it measures how much the sensitivity of price versus yield changes as yields change. As a second order measure, it is approximately proportional to duration squared—in other words, a bond with a duration of 20 years will have approximately four times the convexity of a bond with a duration of 10 years (because 20 squared is four times 10 squared).
How are convexity and cash flows related?
Convexity is directly related to the dispersion of cash flows in time around the Macaulay duration of the bond. For a given Macaulay duration, the lowest convexity bond will be a zero-coupon bond with one cash flow at maturity.
Key rate duration (or partial duration)
Sensitivity of a bond’s price to a change in benchmark yield curve for a specific maturity, while other rates remain the same
it helps to assess exposure to non-parallel changes in yield curves, where different maturity rates move by different amounts .
eg a bond with a 10 year key rate duration of 7 is expected to fall by approximately 7% when 10 year benchmark yields rise by 1% while all other maturity rates stay the same.
Empirical duration
Regressing bond returns versus benchmark yield changes
This is the same interpretation as effective duration, however, it is based on past observed market behavior rather than derived through modelling.
Money Duration
A measure of the monetary gain or loss expected due to 1% change in yield, which is calculated as modified duration x market value
a higher money duration implies a larger absolute change in portfolio value (in currency terms) when yields change by 1%
