Interest Rates P.V. Viswanath - PowerPoint Presentation

1. Interest RatesP.V. ViswanathFor a First Course in Finance1

2. Learning Objectives2What are the determinants of interest rates and expected returns on financial assets?How do we annualize interest rates on loans made for less than a year?What is the difference between real and nominal interest rates?What are yield curves and what can we learn from them?

3. Determinants of Interest Rates3The term interest rate is used to refer to several related concepts.Most commonly, it is the return on a short-term risk-free security (usually a Treasury security).However, it can also be used more generally to refer to the yields (internals rate of return) on longer-term (Treasury) securities.Finally, it is often used to refer to the complex of rates of return on all Treasury securities, and sometimes all bonds.Interest rates are determined, on the one hand, by the productivity of real assets in the economy and, on the other hand, by the time preferences of investors.In fact, expected rates of return on all financial assets are determined by similar considerations.

4. 4Determinants of Expected Rates of Return on Financial AssetsThe expected productivity of capital goodsCapital goods, such as mines, roads, factories are more productive if an initial investment returns in more output at the end of the periodThe degree of uncertainty about the productivity of capital goodsInvestors dislike uncertainty; the greater the uncertainty, the greater the required expected rate of returnTime Preferences of peopleIf people dislike waiting to consume, expected returns will be higher.Risk AversionThe more people dislike uncertainty, the greater the required expected rate of returnExpected InflationThe higher the expected rate of inflation, the greater the required expected nominal rate of returnWe now look more closely at interest rates and inflation rates.

5. Poll: Productivity of Real Assets5In an economy where the return to investment in real assets, such as factories and mines is greater, the interest rate will also be greater.No, if real returns are high, the economy can afford cheaper money. Interest rates will be low.Yes, if real returns are high, deficit institutions, such as corporations which seek funds to invest in these real assets will be willing to pay higher returns and hence the interest rate will be higher.

6. Poll: Uncertainty and Interest Rates6The greater the uncertainty regarding the productivity of real assets like factories, mines and real estate, the greater the interest rate.True, investors need to compensated for the greater risk.False, if the uncertainty is great, then corporations will want to pay less for the use of the funds.

7. Inflation and Nominal Interest Rates7Suppose lenders in equilibrium require a real return of 10% per annum. Suppose, further that the expected inflation rate is 5%, i.e. a unit of consumption costing $1 at the beginning of the year is expected to cost $1.05 at the end of the year.Hence in order to get 10% in real terms, the lender has to ask for a higher nominal rate of return.Now the lender wants 1.1 units of consumption for every unit of consumption given up a the beginning of the year (i.e. $1 which is the price then of 1 unit of consumption).

8. Inflation and Nominal Interest Rates8Suppose he demands 1+r dollars at the end of the period; he will then have (1+r)/(1.05) units at the end of the period. Hence, in order to get a 10% real return, r has to be chosen so that (1+r)/(1.05) = 1.1, i.e. 1+r = (1.05)(1.1) = 1.155 or 15.5%.In general, (1+r) = (1+p)(1+R), where r is the nominal rate, p is the expected rate of inflation and R is the real rate.If the rates are not too high, then this equation can be approximately expressed as r = p+R.

9. Poll: Real rates and inflation9If investors require a real return of 10% p.a. and inflation is expected to be 10% p.a. over the next year, then the nominal 1-year interest rate will be:21% per annum20% per annum0% per annum

10. Effective Annual RateSome time back, we spoke about converting rates of return over multiple years to annual rates. We now look at how to convert rates of return over periods less than a year to annual rates.Suppose you borrow $1 for 1 year; under the terms of the agreement, you are to pay $1.12 at the end of the year.The rate of return obtained by the lender, (1.12-1.0)/1.0 = 12% is called the effective annual rate.Suppose you borrow $1 for 1 month; under the terms of the agreement, you are to pay $1.01 at the end of the period.The rate of return obtained by the lender, (1.01-1.0/1.0 = 1% is called the effective monthly return (EMR).How do we annualize this monthly return?10

11. Effective Annual Rate11One way is to ask what would be the return of the lender over a whole year if the monthly rate of interest continued to be 1% for all 12 months.We know the amount to be paid after one month is 1.01Hence, for the second month, the borrower has to pay interest at the same rate of 0.01 times principal or (1.01)(0.01) of interest for a total of 1.01 of principal plus + (1.01)(0.01) of interest, i.e. (1+.01)(1.01) = (1.01)2. In general, if $K are owed at the end of period i, $K(1+r) will be owed at the end of period i+1. After 12 months, the borrower will owe (1.01)12 = 1.12685. Hence the one-year rate of return for the lender or the effective annual rate of interest is 12.685%

12. Poll: EAR/APR12If a bank charges an interest rate of 1% per month on its loans, the EAR will be:12% per annumGreater than 12% p.a.Less than 12% p.a.

13. EAR and APR13The second way of annualizing is to simply take the EMR of 1% and multiply by the number of periods, which is 12 in this case to get an annualized interest rate of 12%. This is called the APR.However, note that 12% is not the yearly rate of return obtained by the lender!The APR is often used when there is not just one terminal payment over a period less than a year, but a number of equally spaced payments within a year. Thus, the borrower might agree to pay $1 at the end of every month for a year at an APR of 12%We can convert the APR to an EAR, but in order to do that we need to know the frequency of payment. Given an APR of 12% with monthly payments, we first compute the EMR of 12/12 = 1%; this can then be used to compute the EAR as (1.01)12 -1 = 1. 12685 -1 or 12.685%

14. 14The Frequency of CompoundingThe frequency of compounding affects the future and present values of cash flows. The stated interest rate can deviate significantly from the effective interest rate –For instance, a 10% annual interest rate, if there is semiannual compounding, works out to an Effective Interest Rate of 1.052 - 1 = .10125 or 10.25%The general formula isEffective Annualized Rate = (1+r/m)m – 1where m is the frequency of compounding (# times per year), andr is the stated interest rate (or annualized percentage rate (APR) per year

15. 15The Frequency of Compounding Frequency RatetFormulaEffective Annual RateAnnual10%1r10.00%Semi-Annual10%2(1+r/2)2-110.25%Monthly10%12(1+r/12)12-110.47%Daily10%365(1+r/365)365-110.52%Continuous10% er-110.52%

16. 16Computing Monthly Payment on a MortgageWe now see how these concepts can be used to value a mortgage, which involves a sequence of equally-spaced payments (also called an annuity). Suppose you borrow $200,000 to buy a house on a 30-year mortgage with monthly payments. The annual percentage rate on the loan is 8%. The monthly payments on this loan, with the payments occurring at the end of each month, can be calculated using this equation:Monthly interest rate on loan = APR/12 = 0.08/12 = 0.0067

17. Treasury Bills, Bonds and Notes17A T-bill is a promise to pay money 6 months in the future. For example, on Feb. 21, 2008, a 6-month T-bill issued sold for 98.968667 of face value.With the given price then, a buyer would get a 1.042% return for those 6 months.This is often annualized by multiplying by 2 to get an APR (called a bond-equivalent yield) of 2.084%.There are also Treasury bonds (longer maturity) and Treasury notes (medium maturity).

18. Example of a Treasury Note18On Feb. 29th 2008, the Treasury issued a 2% note with a maturity date of February 28, 2010 with a face value of $1000, which was sold at auction. The price paid by the lowest bidder was 99.912254% of face value.This means that the buyer of this bond would get every six months 1% (half of 2%) of the face value, which in this case works out to $10.In addition, on Feb. 28, 2010, the buyer would get $1000.

19. 19TerminologyThe maturity of this note is 2 years.The coupon rate on this note is 2%The face value of this note is $1000The price paid for this note is $999.123The yield-to-maturity obtained by this buyer is 2.045%, i.e. the average rate of return for this buyer if s/he held it to maturity.The yield-to-maturity is just the Internal Rate of Return for the buyer.

20. Yield Curve20The Yield Curve shows the yields-to-maturity on Treasury bonds of different maturities.It shows the maturity on the x-axis and the yield-to-maturity on the y-axis.The yields-to-maturity on treasury securities can be used to estimate the rates on primary securities.These rates can then be used to discount the cashflows of assets, as explained previously.If the asset is risky, then a risk premium has to be added to get the risk-adjusted discount rate.Often, for convenience, if an asset has a life of, say, 10 years, then the yield-to-maturity on a 10-year bond is used to discount all the cashflows on that asset.

21. Yield Curves for March. 3-12, 2014Date1mo3mo6mo1yr2yr3yr5yr7yr10yr20yr30yr03/03/140.040.050.080.120.320.661.462.072.603.273.5503/04/140.060.050.080.120.330.711.542.172.703.363.6403/05/140.060.060.090.130.330.711.542.162.703.363.6403/06/140.060.050.080.120.370.731.572.202.743.403.6803/07/140.060.060.090.130.380.791.652.272.803.453.7203/10/140.050.050.080.120.370.791.642.262.793.453.7303/11/140.060.050.080.130.370.791.622.252.773.433.7003/12/140.050.050.080.120.370.781.592.202.733.383.6621

22. Yield Curves for March 3 to 12, 201422

23. Yield Curves for Feb. 1-12, 200823

24. Poll: Yield Curves24The 10 year annualized interest rate on Treasury securities is usually greater than the 1-year annual interest rate on Treasury securities because:You have to pay a higher return for investors to defer consumption for 10 years than for 1 year.Investors have a short investment horizon. Hence investing for 1 year in a 10-year security exposes you to the risk of whether the bond price will rise (if interest rates in general drop) or fall (if interest rates in general rise).The statement is false. Both rates are usually the same because the term structure is flat.

25. Yield Curve and the Economy25In addition to providing us with discount rates, the yield curve also contains important information.For example, we mentioned above that the nominal interest rate includes an adjustment for expected inflation.The yield curve can be used to extract market estimates of expected future inflation. Furthermore, empirically, the shape of the yield curve correlates with the state of the economy.Thus, an inverted yield curve where long-term rates are lower than short-term rates is usually associated with future depression.