actuarial techniques2 Flashcards
Liability hedging
Liability hedging is where the assets are chosen in such a way as to perform in the same way as the liabilities. In other words, hedging against unpredictable changes in the liabilities that arise from unpredictable changes in the factors that influence liability values.
A specific example of this is the familiar concept of immunisation, where assets are matched to liabilities by term in order to reduce interest rate sensitivity (to parallel movements in the yield curve). Other familiar forms of hedging would include matching by currency and the consideration of the real or nominal nature of liabilities when determining the choice of assets.
However, these examples relate only to specific characteristics of the liabilities, whereas liability hedging aims to select assets which perform exactly like the liabilities in all states.
As such, liability hedging is a halfway house between absolute matching (of the timing and amounts of all the individual cashflows) and immunisation (of the present value of assets less liabilities against changes in interest rates only).
Cashflow matching using bonds
A common method of liability hedging would be for an investor to hold a portfolio of government bonds (in the appropriate currency) until maturity to meet a pre-specified stream of future fixed payments.
A common method of liability hedging would be for an investor to hold a portfolio of government bonds (in the appropriate currency) until maturity to meet a pre-specified stream of future fixed payments.
For example, an investor with five rental payments to make over the next five years might hold five different zero-coupon bonds with terms 1, 2, 3, 4 and 5 years, with maturity payments equal to the annual rental payments.
Provided the future payments do not change in amount or timing, the coupon and principal proceeds from the bond portfolio can be used to meet the obligation to make the payments.
In the example above, the rental payments may well change, eg increase with inflation. This depends on the initial contract and how diligent the landlord is.
Difficulties
Difficulties with this approach arise for the following reasons:
Such an approach requires a bond asset to be held that is equal in present value to the future payments discounted at bond yields (using the full yield curve). Therefore, only a partial hedge is possible if asset cover is less than 100%.
So, it may be that the investor does not yet have the funds to invest because he is intending to earn them in the future.
If the latter payments are payable after the principal payment of the longest available government bond then it will not be possible to hedge these payments at present (until longer maturity bonds become available, ie creating reinvestment risk).
In the UK, this is unlikely to cause too much trouble because government bonds are available for terms of up to 50 years.
Due to “gaps” between bond maturities (particularly at longer durations), there may be a need to reinvest or disinvest bonds prior to maturity, and the hedge may therefore be imperfect.
It may be possible to buy 40-year bonds and 50-year bonds but not 45-year bonds. A 45-year liability could be hedged using a 30-year bond and then using the proceeds at maturity to purchase a 15-year bond. However, if interest rates are unfavourable at the 30-year mark, the proceeds might not be sufficient.
The use of government bonds gives risk to a (small) degree of credit risk that may not necessarily be reflected in the liability.
As mentioned in Chapter 17, Western European government bonds are generally considered to be risk-free assets. However, in recent years, Greece, Ireland and Portugal, among others, have seen their government bonds’ credit ratings downgraded. There is always the possibility that UK government bonds could also be downgraded.
If the tax status of the government bonds worsens, this will mean the assets are likely to be insufficient to meet the liability payments.
Due to the above factors, there may be some mark to market risks between the asset value of the bond portfolio and the present value of the liability payments discounted using the bond yield curve. In some cases this may be a material risk factor, but in other cases this will be much smaller than uncertainties in the liability payments themselves or other portfolio risks.
This approach can be extended to payments that are subject to indexation, provided there are bonds of the appropriate maturity available with the appropriate indexation built into their payment.
Examples
UK index-linked Gilts can be used to meet Sterling RPI-linked payments
US Treasury Inflation Protected Securities can be used to meet US Dollar
CPI-linked payments.
Where there are liquid repo markets on the bonds being used to construct the liability cashflow hedge, repo contracts can be used to release funds. In this way a leveraged exposure to bonds can be created without investing the full market value.
Cashflow matching using bonds and swaps
In markets where liquid and deep interest rate derivative markets have developed, additional flexibility in hedging fixed payments is available through the use of interest rate swaps.
Inflation-linked payments can similarly be hedged using inflation swaps in combination with an interest rate swap. This approach is commonly termed “Liability Driven Investment” (LDI) see Section 2 below.
Using derivatives as opposed to direct investment is often termed synthetic portfolio management. This idea is also discussed in Chapter 20 in the context of tracking an index.
What is the main problem for a UK company investing in index-linked gilts to meet the payments on an annuity?
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Before moving to the next page, suggest some advantages and disadvantages of using swaps to achieve a liability hedge as opposed to direct investment in bonds.
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Advantages of synthetic portfolio management
The use of swaps rather than bonds has the following advantages:
Interest rate and inflation swap markets may have longer maturities
available than bond markets.
Swap markets may have greater liquidity and lower transaction costs than
bond markets.
Swaps permit hedging to be achieved without full asset cover being
required, as they are a contract for difference rather than a funded asset.
Swaps are in most cases bespoke contracts that are agreed with a single counterparty, rather than a standardised listed security (like a bond). Therefore greater flexibility is possible within the schedule of payments.
Disadvantages of synthetic portfolio management
The use of swaps does create the following complications and disadvantages:
If the investor wishes to enter into a swap contract directly then they will need to have ISDA documentation in place with one or more market counterparties (typically investment banks), which is a legal document that is negotiated and can be expensive and time consuming to set up.
If the swaps are subject to collateralisation (to mitigate credit risk), then this will require the movement and investment of collateral on a daily or weekly basis.
The bespoke nature of a swap means that closing out a swap position is more complex than selling a bond. However, in a liquid market closing out a swap may in fact have lower transaction costs than selling a government bond.
Swaps are subject to counterparty risk, if the counterparty bank defaults. Whilst collateralisation will limit losses, if this happens a new swap will need to be put in place at potentially higher cost (replacement risk) or the hedge lost.
Under an interest rate swap, the receiver of the fixed interest rate will need to pay a floating interest rate to the counterparty. To the extent that there is investment risk in the assets that are used to generate the floating rate (eg cash or other assets), the swap will not mitigate these risks, whereas a government bond portfolio is intrinsically low risk from a credit standpoint.
If the swap interest rate curve moves differently to the government bond interest rate curve, this can create a basis risk, which could lead to a mark to market loss.
Other approaches
Other approaches to meeting liability payments are possible, such as holding shorter-maturity assets and “rolling-over” contracts. This may result in a higher yield on assets than investing in long-dated assets or entering into long-dated swaps, however this higher yield will not necessarily lead to a gain as reinvestment terms are uncertain and the “roll over” process may lead to higher transaction costs in the long term.
We described an example of rolling-over above with the idea of using the proceeds of a 30-year zero-coupon bond to purchase a 15-year zero-coupon bond. This process gives rise to reinvestment risk and increased cost.
In principle these approaches can be extended to meeting liability payments that are linked to other indices such as asset indices. Either an over-the-counter derivative can be purchased, or exchange traded derivatives or other assets can be used to dynamically hedge the liability over time by continually rebalancing the portfolio and monitoring “Greeks” (ie sensitivities to various parameters).
This type of process is seen in insurance companies that manage a large number of variable annuity policies or with-profits policies that contain guaranteed annuity rates.
PV01 is used as a measure of the sensitivity of the value of liabilities to changes in interest rates.
PV01 is the
change in present value of the liabilities due to a 1 basis point move in interest rate.
Outline how it might be possible to hedge the liability of a fund that promises to pay a return equal to the increase in the capital value of an equity index over a five-year period subject to a minimum of zero.
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Liability driven investment
Liability Driven Investment (LDI) is the terminology used to describe an investment decision where the asset allocation is determined in whole or in part relative to a specific set of liabilities. LDI is not a strategy or a type of product available in the market but an approach to setting investment strategy.
LDI has gained in popularity since the 1990s and the approach is commonly used by insurance companies and defined benefit pension funds to manage the mismatch between their assets and liabilities (which comprise an income stream to annuitants).
LDI investment strategies have mainly come to prominence in the UK and the US as a result of changes in the regulatory and accounting framework for pension liabilities
Under an LDI approach it is possible to closely match:
the interest rate sensitivity (duration) of the liabilities
the inflation-linkage of the liabilities
the shape of the liabilities
Some investors will focus on matching cashflows, whereas others will focus more on balance sheet hedging ie aligning asset and liability sensitivities under changes in interest rates and inflation expectations. The latter approach is likely to result in an investor accepting a degree of cashflow mismatch in return for lower basis risks.
Implementing an LDI strategy an investor would expect changes in the value of their assets to closely match changes in the value placed on the liabilities.
The liabilities of a pension fund are to employees (future pensioners) and pensioners. Increasingly, pension schemes are becoming defined contribution (DC) as opposed to defined benefit (DB).
What one word best describes investment that is not LDI?
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With a DC schem
e, the liabilities are largely determined by the final asset value so there is more investment freedom. Whereas, with a DB scheme, the liabilities are pre- determined, so there needs to be much more focus on the liabilities and an LDI approach is suitable. The extent to which a scheme focuses on LDI will depend upon the maturity of the fund.
A combination of interest rate and inflation bearing assets can provide a close match of projected benefit cashflows, effectively immunising an investor against future changes in interest rates and inflation expectations.
However, non-investment risks such as longevity tend to remain, although products are being developed to manage non-investment risks and are gaining in popularity.
One such product is a longevity bond, which pays coupons in proportion to the number of survivors in a selected birth cohort, for example individuals turning sixty-five in the year that the bond is issued. Since this payoff approximately matches the liability of annuity providers, these bonds can be used to create an effective hedge against longevity risk.
There are many different approaches to managing LDI,
although most investors tend to focus on:
swap portfolios or
long duration bond management.
Historically, bonds were used as a partial hedge for these interest rate risks but the recent growth in LDI has focused on using swaps and other derivatives. These offer significant additional flexibility and capital efficiency compared to bonds.
