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**DETERMINANTS OF INTEREST RATES**

CHAPTER 2

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**Time Value of Money (TVM) and Interest Rates**

The TVM concept assumes that interest earned over given period of time is immediatelly reinvested: Compounded Suppose you invest $ 1000 Simple interest: For 1 year at 12% interest rate; Value in 1 year: x(0.12)= $1120 For 2 years at 12% int. Rate; Value in 2 years: x(0.12)+1000x(0.12)=$1240

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**Compound Interest. Value in 1 year: 1000+1000x(0.12)= $1120**

Value in 2 years: x(0.12)+1000x(0.12)+1000x(0.12)x(0.12)=$1254.4

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**Alternatively TVM can be used to convert the value of Future cash flow into their Present Values.**

Payments: Lump-sum payment Annuity

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**For Lump-sum payments;**

For Annuities

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**There is a negative relationship btw the interest rates and Present Value.**

There is a positive relationship btw the interest rates and Future Value

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**Effective Annual Return**

The annual interest rate used in the TVM equations are the simple (nominal or 12 month) interest rate. However if the interest is paid and compounded more than once a year, the true annual rate will be the effective (equivalent) annual rate (EAR)

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**Example: What is the EAR on the 16% simple return compounded semiannully?**

What if it is compounded quarterly? r =0.16/4=0.04 EAR=(1+0.04)4 -1 = =16.98%

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Loanable Funds Theory It is the theory of interest rates determination that views equilibrium interest rates in financial markets as a result of supply and demand for loanable funds The supply of loanable funds: Net supplier of funds (households) The demand of loanable funds: Net demanders of funds (corporations and government)

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Interest Rate Supply E Demand Q* Quantity of Loanable Funds Demand and Supply

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**Factors that cause the supply and demand curves for loanable funds shift**

Supply of Funds Equilibrium Int. rate Wealth increases Increases Decreases Risk decreases Near-term spending needs decreases Monetary expansion increases Economic conditions (The flow of foreign funds) increases

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**Utility derived from assets purchased with borrowed funds increases**

Factors Demand of Funds Equilibrium Int. rate Utility derived from assets purchased with borrowed funds increases Increases The lack of restrictiveness of non-price conditions (fees, collateral and etc.) on borrowed funds. Economic conditions (economic growth)

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**Determinants of Interest Rates for Individual Securities**

1) Inflation rate: As actual or expected inflation rate increases, interest rate increases. 2) The real interest rates: It is the rate on a security if no inflation is expected over the holding period Fisher Effect; i = Expected (IP) + RIR

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**Example: One year T-bill rate in 2012 was 4**

Example: One year T-bill rate in 2012 was 4.53% and inflation for the year was 2.80%. If investors expected the same inflation rate, the according to the Fisher effect the real interest rate for 2012; 4.53%-2.80% = 1.73% If one-year T-bill rate was 1.89% while the inflation rate was 3.30%. The real rate; 1.89%-3.30% = %

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3) Default (Credit) Risk: It is the risk that a security issuer will default on making its promised interest and principal payments. As default risk increases, interest rate increases DRP (Default Risk Premiums) = ijt-iTt Bond rating Agencies

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**Example: 10-year Treasury interest rate was 4.70%**

Aaa rated corporate debt interest rate was 5.58% Baa rated corporate debt interest rate was 6.70% Average DRP: DRPAaa= 5.58%-4.70% = 0.88% DRPBaa=6.70%-4.70% = 2%

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4) Liquidity Risk: If a security is illiquid, the investors add liquidity risk premium (LRP) to the interest rate on the security. 5) Special Provisions and Covenants: Such as taxability, convertability and collability affect the interest rates. As special provisions that provide benefits to the security holder increases, interest rate decreases.

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**6) Term to Maturity: Term structure of interest rates (yield curve)**

Maturuiy premium (MP) is the difference between the long and short-term securities of the same characteristics except maturity. Yield curve: Relationship btw YTM and time to maturity.

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**Yields may rise with maturity (up-ward sloping yield curve: the most common yield curve)**

Yields may fall with maturity(Inverted or downward sloping yield curve) Flat yield curve: Yields are unaffected by the time to maturity İJ=f(IP,RIR,DRPJ, LRPJ, SCPJ, MPJ)

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**Term Structure of Interest Rates**

Explanations for the shape of the yield curve fall into 3 theories Unbiased Expectations Theory Liquidity Preferences Theory Market Segmentation Theory

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**1. Unbiased Expectations Theory**

According to this theory, yield curve reflects the market’ s current expectations of future S-T rates. Suppose an investor has a 4-year investment horizon Buy a 4-year bond and earn current yield on this bond, 1R4 Invest in 4 sucessive one-year bonds. You know the 1-year spot rate but form expectations on the future rates on 1-year bond for 3 years, 1R1, E(2r1), E(3r1), E(4r1)

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**Example: Suppose that the current 1-year rate (spot rate), 1R1=1.94%.**

Expected one-year T-Bond rates over the following 3 years are; E(2r1)=3%, E(3r1)=3.74%, E(4r1)=4.10% Using the unbiased exp. theory current rates for two, three and four year maturity T-Bonds should be;

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1R2=[( )(1+0.03)]1/2-1=2.47% 1R3=[( )(1+0.03)( )]1/3-1=2.89% 1R4=[( )(1+0.03)( )( ]1/4-1=3.19%

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**2. Liquidity Premium Theory**

It is based on the idea that investors will hold L-T maturities only if they are offered at a premium to compensate for future uncertainity with security’s value. It states that L-T rates are equal to geometric average of current and expected S-T rates and liquidity risk premium.

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**Example: Suppose that the current 1-year rate (spot rate), 1R1=1.94%.**

Expected one-year T-Bond rates over the following 3 years are; E(2r1)=3%, E(3r1)=3.74%, E(4r1)=4.10% In addition, investors charge a liquidity premium such that; L2=0.10%, L3=0.20%, L4=0.30%,

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**Current rates for 1,2,3 and 4 year maturity Treasury securities;**

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**Market Segmentation Theory**

Individual investors and FIs have spesific maturity preferences, and to get them to hold maturities other than their prefered requires a higher interest rate (maturity premium). For exp banks might prefer to hold S-T T-Bonds because S-T nature of their deposits. Insurance companies might prefer to hold L-T T-Bonds because L-T nature of their liabilities (such as life insurance policies)

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**Forecasting Interest Rates**

Upward sloping yield curve suggests that the market expects future S-T interest rate to increase. So that this theory can be used to forecast interest rates. “Forward rate” is the expected or implied rate on a S-T security. The market’s expectations of forward rates can be derived directly from existing or actual rates on securities currently traded in the spot market.

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1R2=[(1+ 1R1)(1+ 2f1)]1/2-1 2f1=[(1+ 1R2)2/(1+ 1R1)]-1

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Example: The existing (current) one-year, two-year, three-year and four-year zero coupon Treasury security rates; 1R1=4.32%, 1R2=4.31%, 1R3=4.29%, 1R4=4.34%

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**Using the unbiased exp. theory, forward rates on zero coupon T-Bonds for years 2, 3 and 4 are;**

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Problems 20, 21, 22, 23

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