Interest Rate Risk Finance 129
Review of Key Factors Impacting Interest Rate Volatility • Federal Reserve and Monetary Policy • Discount Window • Reserve Requirements • Open Market Operations • New Liquidity Facilities • Quantitative Easing • Operation Twist
Total Assets of Federal Reserve www.federalreserve.gov/monetarypolicy/bst_recenttrends.htm
Federal Reserve Assets - Detailed www.federalreserve.gov/releases/h41
Review of Key Factors Impacting Interest Rate Volatility • Fisher model of the Savings Market • Two main participants: Households and Business • Households supply excess funds to Businesses who are short of funds • The Saving or supply of funds is upward sloping (saving increases as interest rates increase) • The investment or demand for funds is downward sloping (demand for funds decease as interest rates increase)
Saving and Investment Decisions • Saving Decision • Marginal Rate of Time Preference Trading current consumption for future consumption Expected Inflation • Income and wealth effects Generally higher income – save more Federal Government Money supply decisions • Business Short term temporary excess cash. • Foreign Investment
Borrowing Decisions • Borrowing Decision • Marginal Productivity of Capital • Expected Inflation • Other
Equilibrium in the Market Decrease in Income Original Equilibrium S’ S S D D Increase in Marg. Prod Cap Increase in Inflation Exp. S’ S S D’ D’ D D
Loanable Funds Theory • Expands suppliers and borrowers of funds to include business, government, foreign participants and households. • Interest rates are determined by the demand for funds (borrowing) and the supply of funds (savings). • Very similar to Fisher in the determination of interest rates, except the markets for the supply and demand for funds is expanded.
Loanable Funds • Now equilibrium extends through all markets – money markets, bonds markets and investment market. • Inflation expectations can also influence the supply of funds.
Liquidity Preference Theory • Liquidity Preference • Two assets, money and financial assets • Equilibrium in one implies equilibrium in other • Supply of Money is controlled by Central Bank and is not related to level of interest rates (A vertical line)
The Yield Curve Three things are observed empirically concerning the yield curve: • Rates across different maturities move together • More likely to slope upwards when short term rates are historically low, sometimes slope downward when short term rates are historically high • The yield curve usually slope upward
Three Explanations of the Yield Curve • The Expectations Theories • Segmented Markets Theory • Preferred Habitat Theory
Pure Expectations Theory • Long term rates are a representation of the short term interest rates investors expect to receive in the future. (forward rates reflect the future expected rate). • Assumes that bonds of different maturities are perfect substitutes • In other words, the expected return from holding a one year bond today and a one year bond next year is the same as buying a two year bond today.
Pure Expectations Theory: A Simplified Illustration Let Rt = today’s time t interest rate on a one period bond Ret+1 = expected interest rate on a one period bond in the next period R2t = today’s (time t) yearly interest rate on a two period bond.
Investing in successive one period bonds If the strategy of buying the one period bond in two consecutive years is followed the return is: (1+Rt)(1+Ret+1) – 1 which equals Rt+Ret+1+ (Rt)(Ret+1) Since (Rt)(Ret+1) will be very small we will ignore it that leaves Rt+Ret+1
The 2 Period Return If the strategy of investing in the two period bond is followed the return is: (1+R2t)(1+R2t) - 1 = 1+2R2t+(R2t)2 - 1 (R2t)2 is small enough it can be dropped which leaves 2R2t
Set the two equal to each other 2R2t = Rt+Ret+1 R2t = (Rt+Ret+1)/2 In other words, the two period interest rate is the average of the two one period rates
Expectations Hypothesis R2t = (Rt+Ret+1)/2 • Fact 1 and Fact 2 are explained well by the expectations hypothesis • However it does not explain Fact 3, that the yield curve usually slopes up.
Problems with Pure Expectations • The pure expectations theory ignores the fact that there is reinvestment rate risk and different price risk for the two maturities. • Consider an investor considering a 5 year horizon with three alternatives: • buying a bond with a 5 year maturity • buying a bond with a 10 year maturity and holding it 5 years • buying a bond with a 20 year maturity and holding it 5 years.
Price Risk • The return on the bond with a 5 year maturity is known with certainty the other two are not. • The longer the maturity the greater the price risk
Reinvestment rate risk • Now assume the investor is considering a short term investment then reinvesting for the remainder of the five years or investing for five years. • Again the 5 year return is known with certainty, but the others are not.
Local Expectations • Similarly owning the bond with each of the longer maturities should also produce the same 6 month return of 2%. • The key to this is the assumption that the forward rates hold. It has been shown that this interpretation is the only one that can be sustained in equilibrium.* Cox, Ingersoll, and Ross 1981 Journal of Finance
Return to maturity expectations hypothesis • This theory claims that the return achieved by buying short term and rolling over to a longer horizon will match the zero coupon return on the longer horizon bond. This eliminates the reinvestment risk.
Expectations Theory and Forward Rates • The forward rate represents a “break even” rate since it the rate that would make you indifferent between two different maturities • The pure expectations theory and its variations are based on the idea that the forward rate represents the market expectations of the future level of interest rates. • However the forward rate does a poor job of predicting the actual future level of interest rates.
Segmented Markets Theory • Interest Rates for each maturity are determined by the supply and demand for bonds at each maturity. • Different maturity bonds are not perfect substitutes for each other. • Implies that investors are not willing to accept a premium to switch from their market to a different maturity. • Therefore the shape of the yield curve depends upon the asset liability constraints and goals of the market participants.
Biased Expectations Theories • Both Liquidity Preference Theory and Preferred Habitat Theory include the belief that there is an expectations component to the yield curve. • Both theories also state that there is a risk premium which causes there to be a difference in the short term and long term rates. (in other words a bias that changes the expectations result)
Liquidity Preference Theory • This explanation claims that the since there is a price risk and liquidity risk associated with the long term bonds, investor must be offered a premium to invest in long term bonds • Therefore the long term rate reflects both an expectations component and a risk premium. • The yield curve will be upward sloping as long as the premium is large.
Preferred Habitat Theory • Like the liquidity theory this idea assumes that there is an expectations component and a risk premium. • In other words the bonds are substitutes, but savers might have a preference for one maturity over another (they are not perfect substitutes). • However the premium associated with long term rates does not need to be positive. • If there are demand and supply imbalances then investors might be willing to switch to a different maturity if the premium produces enough benefit.
Preferred Habitat Theoryand The 3 Empirical Observations • The biased expectation theories can explain all three empirical facts.
Yield Curves Feb 2012 – Aug 2012 data from www.ustreas.gov
US Treasury Rates May 1990 -Sept 2011 data from www.ustreas.gov
Maturity Yield Spreads1990 - 2011 data from www.ustreas.gov
Impact of Interest Rate Volatility on Financial Institutions • The market value of assets and liabilities is tied to the level of interest rates • Interest income and expense are both tied to the level of interest rates
Static GAP Analysis(The repricing model) • Repricing GAP • The difference between the value of interest sensitive assets and interest sensitive liabilities of a given maturity. • Measures the amount of rate sensitive assets and liabilities (asset or liability will be repriced to reflect changes in interest rates) for a given time frame.
Commercial Banks & GAP • Commercial banks are required to report quarterly the repricing Gaps for the following time frames • One day • More than one day less than 3 months • More than 3 months, less than 6 months • More than 6 months, less than 12 months • More than 12 months, less than 5 years • More than five years
GAP Analysis • Static GAP-- Goal is to manage interest rate income in the short run (over a given period of time) • Measuring Interest rate risk – calculating GAP over a broad range of time intervals provides a better measure of long term interest rate risk.
Interest Sensitive GAP • Given the Gap it is easy to investigate the change in the net interest income of the financial institution.
Example Over next 6 Months: Rate Sensitive Liabilities = $120 million Rate Sensitive Assets = $100 Million GAP = 100M – 120M = - 20 Million If rate are expected to decline by 1% Change in net interest income = (-20M)(-.01)= $200,000
GAP Analysis • Asset sensitive GAP (Positive GAP) • RSA – RSL > 0 • If interest rates h NII will h • If interest rates i NII will i • Liability sensitive GAP (Negative GAP) • RSA – RSL < 0 • If interest rates h NII will i • If interest rates i NII will h • Would you expect a commercial bank to be asset or liability sensitive for 6 mos? 5 years?
Important things to note: • Assuming book value accounting is used -- only the income statement is impacted, the book value on the balance sheet remains the same. • The GAP varies based on the bucket or time frame calculated. • It assumes that all rates move together.
Steps in Calculating GAP • Select time Interval • Develop Interest Rate Forecast • Group Assets and Liabilities by the time interval (according to first repricing) • Forecast the change in net interest income.
Alternative measures of GAP • Cumulative GAP • Totals the GAP over a range of of possible maturities (all maturities less than one year for example). • Total GAP including all maturities
Other useful measures using GAP • Relative Interest sensitivity GAP (GAP ratio) • GAP / Bank Size • The higher the number the higher the risk that is present • Interest Sensitivity Ratio
What is “Rate Sensitive” • Any Asset or Liability that matures during the time frame • Any principal payment on a loan is rate sensitive if it is to be recorded during the time period • Assets or liabilities linked to an index • Interest rates applied to outstanding principal changes during the interval
What about Core Deposits? • Against Inclusion • Demand deposits pay zero interest • NOW accounts etc do pay interest, but the rates paid are sticky • For Inclusion • Implicit costs • If rates increase, demand deposits decrease as individuals move funds to higher paying accounts (high opportunity cost of holding funds)
Expectations of Rate changes • If you expect rates to increase would you want GAP to be positive or negative? • Positive – the increase in assets > increase in liabilities so net interest income will increase.
Unequal changes in interest rates • So far we have assumed that the change the level of interest rates will be the same for both assets and liabilities. • If it isn’t you need to calculate GAP using the respective change. • Spread effect – The spread between assets and liabilities may change as rates rise or decrease
Strengths of GAP • Easy to understand and calculate • Allows you to identify specific balance sheet items that are responsible for risk • Provides analysis based on different time frames.