Liability driven investing for life insurers south
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As a third factor, new pension rights may improve a weakly funded ratio if the actuarial price is paid for these rights. If these mitigating effects are ignored, the resulting asset allocation may become overly conservative given a certain long-term ambition. This paper contributes to the existing literature by examining the consequences of LDI for life insurers. Our approach is similar to Boender 7 in the sense that we use a scenario approach Footnote 10 to study the effectiveness of LDI.
Our results are, however, much more positive and indicate that the LDI concept has several major advantages for life insurance companies:. When setting up a proper LHP, one has to explicitly address all risks embedded in insurance liabilities, including the options embedded in these liabilities. When the liability-driven risks are covered by the LHP, the resulting return assets can be optimised using well-known Markowitz optimisation techniques or equity hedge strategies.
In one sense, constructing LHP portfolios for life insurers is more straightforward than for pension funds since most claims are in nominal terms. The issue of hedging inflation risk is therefore of less importance although exceptions exist, for example in the case of insured pension contracts with indexation. Complicating issues like the effect of risk-sharing with a sponsor and the effect of conditional indexation are also absent or of less importance since typically no sponsor exists and claims are not adjusted to inflation.
Stated differently, for most insurance companies it is clear what the actual liability is and how the market value of this liability should be determined. Footnote In another sense, LDI portfolios for insurance companies are relatively complex compared to LHP portfolios for pension funds due to options embedded in insurance contracts. We demonstrate in this paper that matching these embedded options with the proper financial instruments like swaptions, stock options or other hybrid instruments is possible, although some mismatch risk can of course remain in practice.
We also show that overall risk is determined to a large extent by the market value of the matching assets compared to the market value of the liabilities. If these market values are equal, overall risk is minimised. If the volume of the matching assets becomes smaller than the value of the liabilities, overall risk and return increases strongly because more leverage is created on the return balance sheet. The remainder of this paper is organised as follows. We first explain in the next section how a simple LDI balance sheet can be constructed by rearranging the assets on a separate matching and return balance sheet.
We then investigate in the subsequent section how the matching assets the LHP can be optimised in such a way that the market value of the liabilities is replicated for a large set of economic scenarios. Using this optimised LHP, we study risk and return on the overall balance sheet in the section after that. The last section concludes.
The fair value balance sheet in Figure 1 will serve as an example in this paper. The fair value balance sheet serving as an example in this paper. Note : We here consider a stylised balance sheet of an insurance company with i products without additional optionalities like simple annuities , ii products with additional profit-sharing based on the interest rate level and iii unit-linked investment contracts with guarantees.
The stylised asset mix consists of 70 per cent fixed income and 30 per cent bonds. The fair value reserve first of all consists of a basic reserve for the expected guaranteed premiums, costs and benefits value: We do not include an MVM to keep the analysis a simple as possible. Footnote 12 For simplicity, we also do not consider new business but only the runoff of the existing policies.
This is not to say that the effect of new business can be ignored in practice: for going-concern ALM analyses this aspect should definitely be taken into account. When an insurer has selected an LDI solution it is, obviously, also extremely important to update the LHP for the existing policies with additional liability hedges when new business arrives. For brevity, we also ignore the effect of policy-holders who surrender their policy.
Surrender is an important phenomenon, however, which should be considered in practice. The insurer of this example has a significant number of insurance policies with additional profit-sharing in case of high interest rates.
Because this profit-sharing component is essentially an interest rate option, an additional reserve is required value: Footnote 13 There is also a reserve for embedded options in unit-linked policies value: Footnote 14 These options are important when the policy-holders receive a guaranteed return on their investments or a guaranteed capital when the contract ends insurers must compensate a shortfall with respect to such a guarantee.
As a compensation for giving this guarantee, this insurer receives a fixed guarantee fee. The assets consist of 30 per cent stocks value: and 70 per cent fixed income value: These assets are annually rebalanced to the initial 30 per cent — 70 per cent mix. Currently, no interest rate derivatives or stock options are used by the insurer.
On the basis of this balance sheet, the insurer's surplus is equal to Because the legally required solvency level according to the Solvency I guidelines is equal to 46, the Solvency I ratio is equal to per cent. We now apply the LDI concept and split the balance sheet in a return and a matching balance sheet. Figure 2 shows the effect of this procedure. The insurer's balance sheet, but now from an LDI perspective.
Note : The balance sheet is divided in a matching balance sheet with the liabilities and fixed income. The other assets stocks and the surplus are part of the return balance sheet. Because the value of the fixed income assets is smaller than the market value of the liabilities, a fictive cash position is added to the matching balance sheet. This causes a short cash position i.
Fixed income thus naturally belongs to the LHP, since these assets are used to match the interest rate sensitivity of the liabilities. The remaining assets stocks are part of the RP. This fictive cash position is needed to match the volume of the liabilities. Because theoretically liabilities are exactly replicated by the corresponding assets, the matching assets should have the same volume as the liabilities.
A cash position, which has almost no interest rate sensitivity, can be used to correct a volume mismatch with the liabilities without interfering with the interest rate hedges in the LHP. Note that this cash position also appears on the return balance sheet, but on the opposite side. This implies that we effectively create more leverage on the return balance sheet when the volume mismatch on the matching balance sheet increases.
Due to this added leverage, the risk and the expected return on the return balance sheet increases. The above picture changes if the fixed income investments partly consist of credits. These more risky investments can, however, also be modelled within an LDI framework by decomposing them in a risk-free Treasury bond portfolio plus a stochastic excess term that models the additional risk and return associated with credit bonds.
This stochastic excess term can be modelled conveniently in the RP with a long credits—short Treasury position. An example is given in Figure 3. The effect of credits on the return and matching balance sheet. Note : We here decompose the credit portfolio in a risk-free Treasury bond portfolio and a stochastic excess term.
The fictive Treasury bonds are placed in the LHP; the stochastic excess term is modelled in the RP with a long-short position. We here assume that 50 per cent of all fixed income investments consists of credits. The long credits—short fictive Treasury position in the RP models the stochastic excess term associated with credits. In practice, the construction of LDI portfolios for life insurers is complicated due to embedded surrender options. For example, policy-holders in Europe are often able to surrender their policy in return for the book value of their policy although hefty penalties may apply.
This creates an incentive to surrender the policy when the market interest rate is high and the book value of the contract exceeds the market value. This embedded option, when exercised, can lead to a significant outflow of funds. They also remark that in practice it is difficult to precisely calibrate the scenario-depending surrender cash flows due to limited historical data on the behaviour of policy-holders.
Given a calibrated model, an LDI portfolio could be constructed, however, which counteracts the effect of surrender. Such a portfolio should consist of interest rate derivatives, like caps of payer swaptions, which approximately mimic the contingent surrender cash flows for high interest rate scenarios.
For the construction of an appropriate portfolio with caps and swaptions a replicating portfolio technique can be used. For more information about this technique, see Oechslin et al. Footnote 16 and Schrager. We now analyse the effectiveness of the simple LHP as specified in Figure 2 i. The value of the fixed income assets plus the fictive cash position should theoretically be equal to the value of the liabilities for all future scenarios.
In other words, the surplus of the matching balance sheet should always be equal to zero. As a test, we generate 1, scenarios for interest rates and stock returns and analyse the evolution of the surplus of the matching balance sheet.
Figure 4 shows the results of this stochastic simulation. Evolution of the surplus of the matching balance sheet. Note : We here consider 1, different economic scenarios. Note the negative impact of a decreasing interest rate on the surplus. Obviously, this simple LHP is not robust with respect to future economic developments.
Especially note the negative impact of a decreasing interest rate on the surplus. This scenario is a typical example of a low interest rate scenario see Panel A. To further analyse the interest rate sensitivity of this insurer we evaluate the effect of a parallel change of the interest rate curve at the current point of time The impact of parallel shifts of the interest rate curve on the matching balance sheet.
Note : Note that the interest rate mismatch between assets and liabilities becomes large for low interest rates. Figure 5 clearly shows that there is a large interest rate mismatch between the assets and liabilities, resulting in a strongly negative surplus for low interest rates. We now add a layer of interest rate swaps to the LHP to mitigate the interest rate risk. These swaps are bought a pari i. We select those swaps that minimise the duration mismatch of the assets in the LHP fixed income plus the additional swaps with the basic reserve the guaranteed cash flows.
The effect of this swap construction is shown in Figure 6. The interest rate sensitivity of the basic reserve is now properly matched at the current point in time and a negative surplus is only caused by high option values for low or high interest rates. The impact of an additional swap construction on the interest rate sensitivity of the matching balance sheet. Note : The interest rate sensitivity of the basic reserve is now matched using the existing fixed income assets and an additional layer of swaps.
In Figure 7 we study the impact of this swap construction in a stochastic simulation. In this simulation we also add an additional swap with a maturity of 30 years in each simulation year to further refine the initial interest rate hedge. These additional swaps are also bought a pari. Figure 7 shows that the risk reduction of the swap construction is large.
Note that the interest rate risk of the embedded options is also mitigated because we match the duration annually with a year swap. This method does not remove the interest rate risk completely, however, since swaps are only effective for small interest rate changes. Evolution of the surplus of the matching balance sheet when an additional swap construction is used.
Because the guaranteed cash flows are now adequately matched, the remaining risks at the matching balance sheet are caused by the unit-linked and profit sharing options. The most important risk at this point is the sensitivity of the net unit-linked option to the price of the underlying stocks. This sensitivity is illustrated in Figure 8. The impact of low equity returns on the surplus of the matching balance sheet.
Note : Notice the increasing value of the unit-linked option see Panel C for a dropping stock index see Panel B. This results in a significant decrease of the surplus of the matching balance sheet see Panel D. For the selected scenario the stock index performs poorly in the long run see Panel B.
This results in an increasing unit-linked option value see Panel C and a dropping surplus on the balance sheet see Panel D. We study the effect of partly hedging the option risks in the unit-linked portfolio in Figure 9. When we hedge 50 per cent of the unit-linked option, at each point in time 50 per cent of the option value and 50 per cent of the option cash flows are matched.
A per cent option hedge exactly matches the embedded option. We assume that these synthetic hedges are financed by selling some of the fixed income assets. The 5 per cent percentile line indicates that 5 per cent of the 1, scenarios i. The lower percentiles e. The downward risks are thus significantly reduced. The effect of hedging the unit-linked option on the evolution of the surplus on the matching balance sheet.
By comparing the lower percentiles it becomes clear that the downside risks decrease when the unit-linked option is hedged. Due to the nature of the unit-linked guarantee option a combined equity—interest rate option this hedge portfolio in practice often consists of a mixture of equity put options and receiver swaptions. Footnote 18 Hybrid derivatives may be a cost efficient alternative as well.
See, for example, the recent paper by Walschots and Van Capelleveen Footnote 19 who demonstrate that the downside risk of a pension fund can be hedged efficiently using a receiver swaption whose strike is depending on the stock market index. If the stock market drops, the strike of this swaption increases and the protection against decreasing interest rates improves. The advantage of this form of protection is that only the true risk scenarios a combination of a low stock level and a low interest rate are hedged.
This may be cheaper than hedging the interest rate and equity risk separately. We continue with the final risk source on the matching balance sheet: the profit- sharing option. This is a pure interest rate option. The percentile plot in Figure 10 shows that the risk on the matching balance sheet further reduces when we hedge these risks as well. The remaining mismatch risk is small and mainly due to the simple duration matching procedure only once a year a new swap is bought.
We have again used a synthetic option here, which exactly matches the option cash flows and option values. Additional experiments show that in practice a good profit-sharing hedge can also be constructed using a set of payer swaptions.
The effect of hedging the profit-sharing option on the evolution of the surplus. Note : This percentile plot shows that the downside risks further decrease when this option is hedged. We started with the simple LHP in Figure 2 , consisting of only a fixed income portfolio in combination with a fictive cash position.
We found that the mismatch of this portfolio with the actual liabilities is huge due to: i a duration mismatch; and, ii profit-sharing and guarantee options that are embedded in the liabilities. The duration mismatch can be minimised efficiently using a layer of linear swap contracts.
In addition, a year swap is bought in each future year to update this initial hedge. The embedded options can be matched by nonlinear products such as payer swaptions for the profit-sharing option or a mixture of receiver swaptions and equity put options or hybrid options for the unit-linked guarantees. The resulting, optimal LHP portfolio is shown in Figure It is important to note that with a relatively modest investment 63 the downside risks on the matching balance sheet can be reduced significantly.
Note : A layer of swaps is bought a pari i. In addition, a year swap is bought in each future year to update this initial hedge these instruments are not visible on the initial balance sheet. The embedded profit-sharing and unit-linked options are hedged using synthetic options which mimic the behaviour of the embedded options in the liabilities. Note : Note that the downward risks on the matching balance sheet are reduced significantly by adding swaps and hedges for the unit-linked and profit-sharing options in the liabilities.
Interestingly, the added option hedges do not appear to have a negative impact on the average surplus on the matching balance sheet compare the average values in Panels A and B. In fact, the average surplus increases slightly because the strongly negative scenarios are almost entirely eliminated the upside scenarios are also suppressed, but this effect is less pronounced. Setting up a proper LHP portfolio thus appears to be very attractive: the downside risks are suppressed significantly, while the average return of the LHP plus the fictive cash position remains sufficiently high to match the expected return of the liabilities.
We now proceed with an analysis of the complete balance sheet. For simplicity, we consider the stylised situation in which the insurer does not pay taxes or dividends. The results are shown in Figure Evolution of the surplus for 1, different economic scenarios.
Panel A shows the evolution of the surplus in case of the original balance sheet in Figure 1. Small differences occur, however, because annual rebalancing has a different effect when we consider a single balance sheet with annual rebalancing as in Panel A or two different balance sheets as in Panel B. Panel C clearly shows the effect of the optimised LHP in Figure 11 : the downside risks are reduced significantly.
To further reduce the risks, we can reduce the percentage of stocks and invest more money in fixed income. This has almost no impact on the risks on the matching balance sheet because the interest rate risks are minimised by the swap construction in the LHP. Footnote 21 The impact on the RP balance sheet is significant, however, because the amount of leverage decreases as well as the allocation to stocks. This effect is illustrated in Figure 14 , where we show the evolution of the surplus on the matching and total balance sheet.
Impact of the volume of the liabilities that is matched by the LHP. Note : In Panel B and D the volume of the liabilities is completely matched with fixed income. This has almost no effect on the mismatch risk on the matching balance sheet compare Panel A with Panel B. The effect on the total balance sheet is significant, however, because leverage on the RP balance sheet is eliminated in Panel B and D and the allocation to stocks decreases.
This reduces both the downside risk and the expected return. In Panels A and C we consider the situation in Figure 11 , where 87 per cent of the volume of the liabilities is matched with fixed income. In Panels B and D we consider the situation where per cent of the volume of the liabilities is matched i. Comparing Panel C with Panel D shows that the downside stock risk decreases when we reduce the amount of leverage and the exposure to stocks.
The way that they do this is built on twin pillars : underwriting, and investment income. Underwriting incomes come from underwriting revenues from the cash collected on insurance policy premiums, minus money paid out on claims and for operating the business. Keep in mind that insurance companies go to great lengths to ensure that they are set up to make money, by using key metrics and other devices to make sure they are set up for success. Insurance companies work very hard on crunching the data and algorithms that indicate the risk of paying out on a policy.
If that data tells them the risk is too high, they either deny the insurance policy or create a premium high enough to ensure profitability. If the data tells them the risk is low, then they will comfortably write a policy with the knowledge that paying out will be low. Insurance companies also make a boatload of money from investment income.
When an insurance company receives its monthly premiums, the insurance company takes those monies and invests them in the financial markets, to increase their revenues. A large portion of the investment income is invested in the bond market, either in government or corporate bonds, thus insurance companies are among the largest investors in the bond markets and are sensitive to changes in interest rates.
Life insurance companies typically have a much higher proportion of fixed assets like bonds, versus equities. What is insurance float, you ask? Well, this is a term that Warren Buffett has made famous, albeit not one that he invented. He has credited it with his ability to generate quite a lot of wealth for himself and his shareholders. Insurers start investing insurance premiums as soon as they are collected and continue to earn interest or other income on them until claims are paid out.
In short, a float is the money that an insurance company gets to hold between the time customers pay premiums, and the time customers make claims on their policies. This from the Oracle of Omaha on the insurance float :. If premiums exceed the total of expenses and eventual losses, we register an underwriting profit that adds to the investment income produced from the float.
This combination allows us to enjoy the use of free money — and, better yet, get paid for holding it. This loss, in effect, is what the industry pays to hold its float. Usually, this cost is fairly low, but in some catastrophe-ridden years the cost from underwriting losses more than eats up the income derived from the use of float. That pretty much sums up insurance float, and is particular to the insurance industry at this point. No other business that I am aware of exhibits the ability to generate a float that they can use to create income for themselves.
How we calculate insurance float is a little complicated, and we will tackle that in a future post. For now, it is enough to understand what it is and how it works. The terminology can be different, and I thought it might be a good idea to flesh the terminology out a little bit. For insurance companies, we are going to start with the Income Statement because everything flows from the premiums that insurance companies collect from their customers. On the expense side, you assume that each dollar of earned premiums carries with it a certain percentage in the claim and claim adjustment expenses.
On top of all that, insurance companies often re-insure policies of other insurance companies, and, in turn, often have other insurance companies re-insure their policies. Got all of that? I know it is a little confusing, but like any exercise, as you use it more, the more you will get comfortable with these terms. I know there are some unfamiliar terms here, but we need to address the liability side, and then we will tackle the asset side.
Ceded Unearned Premiums means the Unearned Premium Reserve, but for policies you have ceded to other insurance companies. The last one, Deferred Acquisition Costs , is simpler: each year, you have to pay a commission on written policies that were referred to you by brokers and salespeople. Good news is that after all the differences in the income statement and balance sheet when we arrive at the Cash Flow Statement, it is set up like any other publicly-traded company.
How to read insurance companies financial statements is important for us to be able to value these companies. As you have seen, the accounting terms are different, but once you understand the terms and what they stand for, it is easier to pick out what is important. A few of these are going to be metrics that will be familiar to a lot of you, the oldies but goodies section. You can calculate the price to book by taking the market price per share, which is easy to find; any stock market app will give you the price.
Calculating the book value per share means that we take total assets subtract them from the total liabilities and divide that by the number of shares outstanding. It excludes intangibles assets like patents or goodwill. In the banking world and the insurance world, this metric is used quite frequently.
The formula for Price to Tangible Book Value is calculated by dividing the price per share by the tangible book value. You can find the tangible book value by subtracting the intangible assets like patents, goodwill, etc. The higher, the better, and a ratio in the mid-teens is ideal for a well-run insurance company. For more details on how to calculate this formula, please follow this link for a more in-depth look into this formula.
The last ratio we are going to look at is the combined ratio, for which I will give you a brief overview. A more in-depth post on the combined ratio can be found here. For our purposes here, the combined ratio measures the incurred losses and expenses as a percentage of earned premiums.
We can calculate the combined ratio by adding the loss ratio and expense ratio, calculating the loss ratio by dividing the incurred losses, including the loss adjustment expense, by earned premiums. You calculate the expense ratio by dividing the incurred underwriting expenses by the earned premiums. Now that we have spent some time researching how insurance companies work, how they make money, and what kinds of metrics to use to value a company.
Founded in , Allstate specializes in auto, home, renters, commercial policies. Price to book for Allstate is currently 1. All of which based:. Hopefully, you could follow all of that; it is pretty easy once we plug in the numbers, which by the way we can gather all of them from the balance sheet. Next up on our list is to calculate the Return on Equity for Allstate. We will gather all of our information from the section titled Summarized financial data on page 41 of the k.
It tells us that Allstate that is operating with a profit from their insurance operations, the lower the number, the better. By now, we have worked through a few ratios which have given us a good idea of the profitability of our business, as well as how they operate by looking at different sections of each financial statement.
The last step to determining whether or not our insurance company is a viable investment for us is to try to determine an intrinsic value.