Week of February 25thFinance 301S.I.1. Define nominal rate of interest (r), real risk free rate of interest (r*), and nominal risk free rate(rrf).Nominal- measured in amount, not in real value. The quoted or stated rate. r= the quoted or nominal rate of interest on a given security.Real risk free r*- rate of interest that would exist on default free US treasuries if no inflation was expected. (B/C U.S. treasuries only have inflation risk)Nominal risk free rate rRF- the rate of interest on a security that is free of all risk: rRF is proxied by the T-bill rate or the T-bond rate. rRF includesan inflation premium.2. What are all of the determinants of interest rates? Write the equation for “r.”The determinants of the interest rate “r” are as follows- Inflation Premium: IP- a premium equal to expected inflation that investors add to the real risk free rate of return. (higher inflation=higher IP)- Default Risk Premium: DRP- the difference between the interest rate of a U.S. Treasury bond and a corporate bond of equal maturity and marketability. (reflects the likelihood of default; higher likelihood = higher DRP)- Liquidity Premium: LP a premium added to the equilibrium interestrate on a security if that security cannot be converted to cash on short notice and at close to its “fair market value.” (the longer it takes to get it to cash, the higher the LP, & the further away from its market value, the higher the LP)- Maturity Risk Premium: MRP- a premium that reflects interest raterisko Interest rate risk- risk of capital losses due to changing interest rates over timeo The longer the security must be held, the higher the MRPThe equation for “r” is: r= r* + IP + DRP + LP + MRP3. Fill in the following table by placing a check mark indicating which premiums are included in which of the following securities.Interest PremiumMaturity Risk PremiumDefault Risk PremiumLiquidity PremiumST Treasury xLT Treasury x xST Corporate x x xLT Corporate x x x x 4. 30 day T-bills are currently yielding 5.5%. The following are current expected interest rate premiumsInflation Premium= 3.45%Liquidity Premium= 0.76%Maturity Risk Premium= 1.65%Default Risk Premium= 2.45%What is the real risk free rate of return? Yield= r = 5.5%T Bill Rate= r* + IP5.5% = r* + 3.45-3.45 - 3.452.05= r*5. Suppose 2 year Treasury bonds yield 5.5%, while 1 year bonds yield 4%. r* is 1.5% and the maturity risk premium is 0.Using the expectations theory, what is the yield on a 1-year bond, 1 year from now?Expectations theory- the shape of the yield curve depends on the investor’s expectations about future interest rates. If interest rates are expected to increase, long term rates will be higher than short term. If interest rates are expected to decrease, short term rates will be higher long term rates.(1.04) (1 + X) = (1.055)2Take (1 + I for 1 year) * ( 1 + X) = (1 + Interest rate in year 2)2(1.04) (1 + X) = 1.113025/1.04 /1.041 + X = 1.0702-1 -1X= .0702 or 7.02%6. A company’s 5 year bonds are yielding 7.85% each year. Treasury bonds with the same maturity are yielding 4.82% per year, and the real risk free rate (r*) is 2.3%. The average inflation premium is 2.5% and thematurity risk premium is estimated to be 0.1 X (t-1)% where t= years to maturity. If the liquidity premium is .8%, what is the default risk premium on the corporate bonds?r= r* + IP + DRP + LP + MRP7.85= 2.3 + 2.5 + DRP + .8 + (.1) (5-1)7.85= 2.3 + 2.5 + DRP + .8 + .47.85= 6 + DRP-6 -61.85%= DRP7. The real risk free rate is 4%. Inflation is expected to be 2.5% in year one, 3.4% in year two and 5% each year following. The maturity risk premium is 0.05 (t-1)%. (t= number of years to maturity) What is the yield on a 6 year treasury note?r= r* + IP + DRP + LP + MRPr*= 4%IP= (2.5 + 3.4 + 5(4))/ 6 = 4.31667 or about 4.32%MRP= .05 (6-1) = .25%DRP= 0LP= 0r= 4 + 4.32 + .25=