1. Financial Risk Management of Insurance Enterprises
Forward Interest Rates

2. Overview What are forward rates of interest?
How do you develop forward rates?
What is the relationship between forward rates and spot rates?
What is meant by the term structure of interest rates?
What theories exist to explain the term structure shape?

3. Forward Rates - A Definition
“Market consensus” of future interest rates
Also known as implied forward rates - they are derived from the Treasury yield curve
Any future period has a forward rate
End of forward period must have a spot rate
Typically, forward rates are calculated on bond maturity dates
e.g., we used semi-annual maturities last time

4. Notation

5. Example
An insurer has issued a two year CD and has two investment alternatives
1. Buy a one-year, 5% zero coupon Treasury and reinvest all the proceeds at maturity
2. Buy a two-year, 6% zero coupon Treasury
Which investment should the insurer choose?

6. Example (p.2)
Insurer is indifferent if:

7. Example - Enter Forward Rates
From the Treasury curve (above), the current spot rates imply that the market consensus of the future rate of interest is %
If insurer thinks that the spot rate one year from now will be less than %, it will use the two-year, zero coupon strategy
In the first strategy, the insurer is exposed to the risk of a decrease in the interest rate

8. In General
Use first principles of interest theory to find any forward rate
For example, to determine the 5-year forward rate, 2 years from now:

9. Relationship Between Spot Rates and Short-Term Forward Rates
Extending the previous discussion to short-term forward rates:

10. Consequences
Yield rates, spot rates, and short-term forward rates are all different ways to convey interest rate information
Discounting cash flows is most easily performed using either spot rates or short-term forward rates

11. Are Forward Rates Really a “Market Consensus”
Studies show that forward rates do not predict future interest rates well
Help investors measure expectations relative to the market
Our insurer can speculate, if desired
We will see in a future class that there are financial instruments based on forward rates
Insurer may be able to hedge interest rate risk
Forward rates are really hedgeable rates

12. Term Structure Four historical shapes:
Relationship of interest rates and maturity
Four historical shapes:
Normal (upward slope)
Inverted
Humped
Flat
What explains the shape of the term structure?

13. Pure Expectations Theory
Assumes forward rates are expectations of future interest rates
What does this mean for inverted yield curve?
No other systematic explanations predicting shape
If investors believe interest rates will rise, they prefer short-term bonds, selling long-term bonds

14. Biased Expectations Theory
Forward rates are expected future rates plus some other systematic factor
Liquidity Theory
Investors prefer short bonds and require a “liquidity premium” for holding longer bonds
Preferred Habitat
Borrowers/lenders want to be long/short
Each requires premium to shift maturity

15. Market Segmentation
Similar to preferred habitat due to maturity preferences
Banks are main users of short-term funds
Life insurers and pension funds are users of long-term funds
Supply and demand among suppliers/users determines market rates

16. Modeling Interest Rates
Interest rates move randomly
Need statistical representation of stochastic process
One-factor model describes short-term movements
All other rates related to short term rate
Two factor model has additional variable
short term and long term movements
short term level and short term volatility

17. Next time... Forward contracts Foreign exchange forwards
FRAs - forwards on interest rates
Applications of forwards in financial risk management