Feldblum - Asset Liability Matching for P&C Insurers

Question 1

What are the five crucial differences between the characteristics of P&C and life insurance operations?

Answer 1

1. Traditional life insurance and pension fund liabilities are expressed in nominal terms. P&C loss are determined at the settlement date => P&C liabilities are inflation sensitive.
2. For P&C insurer, CFs are generally of shorter duration. This means P&C insurers who follow asset-liability matching will have to invest in short duration assets whose return also vary directly with inflation, such as Treasury bills and commercial paper. But these assets have lower returns than long duration assets with a normal upward-sloping yield curve. => there is a trade-off between the extra yield from longer duration bonds and the extra protection against interest rate sensitivity of surplus.
3. Equity cash flows and P&C liabilities share two similarities - both are inflation sensitive and both are subject to considerable risk other than interest rate risk (For common stock, it is systematic stock market fluctuations. For insurance liabilities, they are contagion risks and changes in legal interpretation of coverage.)
4. Unlike life insurers, P&C insurers do not face disintermediation risk. P&C insurers expect a steady stream of premium inflow and do not segment funds.
5. Measurements of asset risk often concentrate on nominal returns. Long-term bonds are risky assets for P&C because P&C insurers depend upon real returns except for statutory financial statements.

Question 2

Describe the two matching techniques.

Answer 2

1. Cash flow matching - An insurer’s expected cash flow from its o/s liabilities are exactly matched with fixed cash flow from assets purchased to fund liabilities.

creates an asset/liability portfolio impervious to interest rate changes.

Disadvantages: lower yield, high transaction cost,

constraint in bond selection, only protects against nominal values,

2. Duration matching - Duration of assets matches the duration of o/s liabilities.

hedges against small interest rate changes. - A change in new money interest rates has two effects on bond prices i). coupons are reinvested at higher/lower returns ii). bond’s price declines when rates rise, and rises when rates fall. - One date when the change in the bond’s market value just balances the change in its reinvestment returns: Macaulay duration.

Disadvantages: only protect against small interest rate change, only protect against parallel shift in term structure, need to rebalance portfolio, does not hold if inflation change.

Question 3

A loss reserve duration can be calculated using

Answer 3

a payout pattern developed from Schedule P and

using current bond interest rates, since bonds form such a large % fo an insurer’s investible assets

(assume mid year liability payments)

Loss Reserve Duration = Σ (t-0.5)*CF_t*(1+y) ^-(t-0.5) /ΣCF_t*(1+y)^-(t-0.5)

Question 4

Why is macaulay duration misleading for asset/liability matching?

Answer 4

Although asset-liability managment mitigates the risk of interest rate chagnes, duration matching does not. Asset-liability matching does not accout for the effects that interest rate changes have on loss payments. This is due to the fact that P/C insurance liabilities’ payments are inflation sensitive.

Question 5

Inflation Sensitive Cash Flows

Answer 5

A. Cash flows from GL losses are uncertain, and inflation sensitive.

B. If liability losses are sensitive to inflation through the settlement date, then the reserve is equivalent to an asset with a duration of 0 years.

To eliminate the influence of interest rate chagnes on net worth, one should

1. Invest in ST securities or
2. Invest in securities that are also inflation sensitive

C. Most reserves are not fully inflation sensitive through the settlement date.

1. WC payments are largely fixed at the accident date
2. Auto BI wage loss and medical bills may be determined soon after the accident.

Question 6

What are the three reasons that P&C insurers invest heavily in long-term bonds?

Answer 6

1. Higher Returns: high quality, long-term bonds usually yield more than short term commercial paper
2. Lower Transaction Costs: the least amount of transaction costs are incurred when purchasing long-term bonds and hold to maturity
3. Disintermediation: P/C insurers do not face disintermediation risk

Question 7

Three traditional investment concerns remain paramount:

Answer 7

• Maximizing expected returns.
• Ensuring safety of principle.
• Balancing the risk of each class of securities.

Question 8

Both property and liability reserves have low durations, but for different reasons. What are the reasons?

Answer 8

Most liability reserves are infaltion sensitive; they are equivalent to short duration assets.

Property reserves are not infaltion sensitive, they have short durations as they are paid out quickly.

Question 9

Short term commercial paper has a duration similar to that of GL loss reserve. What are the two problems when investing short-term commercial paper?

Answer 9

1. it generates low yields
2. high transaction costs

Question 10

Correlation between Inflation and Bonds

Answer 10

Market price of bonds varies strongly and inveserly with inflation rates.

The correlation is reduced when LT bond captail gain is lagged one year. The reduction results from two factors:

1. MV of bonds move toward their face value as the time to maturity shortens
2. Newly issued bonds are not affected by past changes in interest rates.

There is no “rebond” from the initial decline in MVs.

Question 11

Correlation between Inflation and Stocks

Answer 11

Common stock varies weekly and inversely with inflation rates.

There is a “rebound” from the initial decline in MVs.

• initial acceleration of inflation hurts most firms, buth then firms adjust their costs and prices so that nominal common stock value vary directly with recent inflation.

Common stocks are similar to casualty reserves: both track the real value of money

Common stocks are similar to liability reserves: both changes with interest rate

Question 12

Which among the four specific investments does Feldblum conclude is the apparent investment of choice.

Answer 12

Since cash flows from most liability loses are sensitive to infaltion through the settlement date, the loss reserve is equivalent to an asset with a duration of zero years. Therefore, to invest in either short term securities (commercial paper and Treasury Bills) or in securities that are also inflation sensitivie (common stocks or real estate).

Yields on commercial paper and Treasury Bills are too low.

Real estate are limited by regulation and too risky.

Therefore, common stocks are the apparent choice.

Question 13

Section 12.2 Conclusions

Answer 13

addd

Question 14

Why are interest rate changes not a serious risk fro stable P/C insurers?

Answer 14

Stable P&C insurers generally hold long-term bonds to maturity. Regardless of interest rate changes, insurers use current premium income and investment income to pay claims. Insolvency is caused by other problems, such as inadequate rates or incompetent management. Duration mismatch only exacerbates the problem. It rarely causes insolvency.