Managing Financial Risk for Insurers Term Structure of

Managing Financial Risk for Insurers Term Structure of Interest Rates Forward Contracts Foreign Exchange Forwards FRAs - Forwards on Interest Rates Applications of Forwards in Financial Risk Management

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

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 longterm bonds

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

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

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

Basic structures of financial instruments used to manage financial risk • • • Forwards Futures Swaps Options Interest Rate Options: Caps and Floors

Forward Contracts • Basic structure and definition • Foreign Exchange (FX) forwards and interest rate parity (IRP) • Forward rate agreements (FRAs) • Applications of forwards in protecting against financial risk

Forward Contract Structure • A forward contract is an agreement which obligates one party to sell and asset and another party to buy the assets. The exchange will take place some time in the future, but the price is fixed today. • The exercise price is the contract price • The buyer of a forward is long a contract, the seller of a forward is short a contract

Comments • No payment until maturity • Forwards occur everywhere – Sign apartment lease or buy a home • Buyer of forward has a gain if underlying asset value increases – Buy asset at exercise price and can sell in market • The contract price is set at origination so that the value is zero

Some Forward Contract Jargon • Cash-settle: Value is paid in cash rather than physically exchanging the asset • Notional principal or amount: Used to determine the value of the contract - the notional amount is not exchanged – Used in cash settlements • At-market forward: A forward contract whose value is zero – Spot price and forward prices are equal

Example - Foreign Exchange Forward • Party A agrees to buy and Party B agrees to sell £ 1 million in 6 months at an exercise price of $1. 50/£ – £ 1 million is the notional principal • If the £ strengthens (increases in value), Party A will have a gain • If £ weakens, Party A will have a loss

Example (p. 2) • Let’s assume cash settlement – Rather than actually exchanging the foreign currency, the parties exchange the gain/loss • Case 1 - £ strengthens – Party B pays Party A (PT - $1. 50/£)x(£ 1 million) where PT is the spot exchange rate in 6 months – PT=$1. 60/£, Party A receives $100, 000 • Case 2 - £ weakens – Party A pays Party B ($1. 50/£ - PT)x(£ 1 million) – PT=$1. 00/£, Party A pays $500, 000

Illustrative Forward Contract (Figure 6 -1 of Smithson text)

Payoff for Forward Contract Positions (Figure 6 -2 of Smithson text)

Default Risk • Remember, all exchanges are made at maturity • If the price of the forward contract moves against a party, they may have difficulty making payment • Forwards are pure credit instruments – You must evaluate the counterparty similar to a bank loan

Interest Rate Parity • Spot rates, forward rates and interest rates are related to eliminate arbitrage • Assures that the net present value of a FX forward is zero • Essentially, investing money in any currency should have similar returns • If 100¥ = $1, then 100¥(1+r¥)=$1(1+r$)

Determining the Foreign Exchange (FX) Forward Rate • Can replicate forward contract with the following transactions – 1. Borrow $ for t years at a rate of r$ – 2. Convert $ to ¥ at exchange rate S 0 – 3. Invest ¥ at r¥ for t years – 4. Convert ¥ back to $ and payback loan (can use forward market to lock in exchange rate FT) • Set FX forward rates to guarantee that NPV=0

Determining the Foreign Exchange (FX) Forward Rate (p. 2) • Thus, to prevent arbitrage

Example • What is today’s spot rate in terms of ¥/$ if r$ = 10%, r¥ = 3%, and FT=100¥/$1 – Assume all maturities are one year

Forward Rate Agreement (FRA) • Forward contract on interest rates – Not a commitment of borrowing or lending • Like any forward, value for buyer increases as underlying increases – Here the underlying is an interest rate • Payoff based on difference between market interest rate at settlement and the contract rate • Gives protection against uncertainty in future interest rates

FRA Contract Settlement Value • Contract period is the future period for which protection is needed • Change in market rates affects interest over the contract period • Payment at settlement date reflects discounting

FRA Contract Settlement Value • On 2/12, an insurer enters an FRA contract for the period of 7/1 -12/31, the contract rate is 5%, and the notional amount is $1 million • If on 7/1 rates are 6%, a borrower without an FRA would pay $1, 030, 000 on 12/31 • With an FRA, the amount of payment on 7/1 reflects PV of excess interest throughout contract period

Application of Forward Contracts • US pension fund invests in 6 -month, German zero-coupon bonds with a face value of DM 1 million – Exposure is increase in DM/$ exchange rate • Pension fund can fix the exchange rate today by selling DM 1 million forward • If DM/$ increases, gain in forward contract offsets loss on DM denominated bond holding

Application of FRAs • Life insurer has fixed policy loan rate that resets every year • Exposure is that in 2 nd half of policy year, rates will increase and policyholders withdraw cash to earn higher interest elsewhere • Purchase of FRA with 6 month settlement will mitigate risk – Rates increase, insurer receives cash – Rates decrease, FRA payment from bond gains

Next time. . . • • • Futures contracts Difference between forwards and futures Hedging with futures Basis Risk Applications of future contracts