A market is a place where goods and services are exchanged. Financial Markets A market is a place where goods and services are exchanged. A financial market is a place where individuals and organizations who want to borrow funds are brought together with those having a surplus of funds.

We can classify markets Based on: Underlying asset Delivery date Maturity Players Physical/Financial/Derivatives Spot/Futures Money/Capital Primary/Secondary Private/Public

London Gold Market physical, spot New York Stock Exchange Examples London Gold Market physical, spot New York Stock Exchange financial, spot, secondary, capital Sale of commercial paper by HP financial, money, primary

How is capital transferred between savers and borrowers? Direct transfers Investment banking house Financial intermediaries A firm’s selling its stock directly to another firm/individual is an example of direct transfer

Through Investment bankers Investment banking firm helps a company in the design and sale of securities. The investment banker is also called the underwriter. The agreement between the firm and underwriter can be of two types: firm-commitment basis: underwriter bears all the risk best-efforts basis: underwriter does not buy the issue but acts as a selling agent

Through Investment bankers In general, the lead investment banker puts together a purchase group and a selling group purchase group underwrites the offering (purchases securities from the issuing corporation) selling group contacts potential buyers and do the selling on a commission basis Examples of Investment Banking Firms: Merrill Lynch, Salomon Smith Barney

Examples of financial intermediaries Commercial banks Pension funds Life insurance companies Mutual funds Financial intermediaries get savings from individuals by creating new financial products For example, commercial banks open checking and saving accounts, life insurance companies sell policies and mutual funds sell new shares and are ready to buy back outstanding shares.

financial intermediaries Strengths of financial intermediaries Economies of scale in analyzing creditworthiness of potential borrowers Pooling risk

Mutual funds Mutual funds differ in their investment objectives, e.g. Pursue Aggressive growth Invest in Precious metals Invest in Global equity Turkish: type A minimum 25% investment in stocks, it may also include fixed income securities. Type B investment only in fixed income securities. Type B liquid funds limit maturity up to 90 days. Ranking of Mutual Funds (US): Lipper Ranking Morningstar Ranking Each fund is ranked within the universe of funds similar in investment objectives

Physical location stock exchanges vs. Electronic dealer-based markets Auction market vs. Dealer market (Exchanges vs. OTC) Exchanges can have continuous trading, call auctions or both Mostly: Continuous-auction also contain opening call How do they provide continuity: Limit Order Book Liquidity: conversion to cash quickly, with low cost, and for reasonable transaction sizes

Physical location stock exchanges vs. Electronic dealer-based markets Members have seats (e.g. NYSE ≈1400 members) Only members can execute transactions Over-the-counter (OTC) market e.g. Nasdaq Several dealers assigned to each stock They quote bid/ask prices Computerized system Dealers hold inventory

Cost of Money except social, strategic policies capital is allocated through a price system debt capital: interest rate equity capital: dividend yield capital gains

Four fundamental factors Production opportunities Time preferences for consumption Risk Inflation Different markets Interest rates differ due to differences in risk, but the rates are interrelated

Determinants of Market Interest Rates rate = k* + IP + DRP + LP + MRP k*: real risk-free rate IP: Inflation Premium DRP: Default risk premium LP: Liquidity premium MRP: Maturity risk premium

Determinants of Market Interest Rates Inflation is expected future inflation, not the past rate Default: The borrower will not pay the interest or principal, probably because of financial distress Liquidity: being able to sell the security quickly at fair market value

Determinants of Market Interest Rates Government securities e.g. T-bonds have basically no DRP and little LP. They are only subject to IP and MRP Maturity risk premium: Extra return offered by securities with longer time to maturity. Bond prices are negatively related to interest rates. In other words, as interest rate rises, bond price will fall.

Simple example A security that has a single payoff of $110 in one year. If the market price of this security is $100, what is the promised return? If the market price of this security is $90, what is the So a decrease in price increases return.

For example Interest rate (promised return)=10% and bond price=$920 now I own this bond but I have just decided to sell it (I need cash). If interest rate rises to 12% (market prices similar securities so that their promised return rises to 12%), price of the bond will fall. So I and other bondholders will have a loss due to a fall in price when interest rates rise. This is called as the interest risk. When I sell the bond at the new (lower) price, the buyer will have a promised return of 12%. The amount and the timing of payments made by the issuer of the bond to bondholders are fixed. The market price is the only bond feature that can change. So to raise the promised return from 10% to 12%, the price of the bond has to fall.

interest rate risk For a given holding period, the interest rate risk as measured by the price change at the end of your holding period increases with the time to maturity of the bond. So other things being equal, a bond with 20 year time-to-maturity will have larger MRP than that of a 10 year bond.

reinvestment rate risk We did ignore another type of risk, the reinvestment rate risk from the discussion above. Actually, MRP is the net effect of interest rate and reinvestment rate risks. We will return to this discussion after we cover the Time Value of Money concept.

Ratings Bond Rating Agencies: Moody’s and S&P Attributes associated with better ratings Lower financial leverage Larger firm size Larger and steadier profits Larger cash flows Lack of subordination to other debt issues

Term Structure of Interest Rates The relationship between short term and long term interest rates is known as term structure of interest rates Yield curve: graph showing the relationship between bond yields and maturities

e.g. Yield Curve for Government securities (DRP=LP=0) 5 10 15 1 20 Years to Maturity TTM rate/year 1 yr 8.0% 10 yr 11.4% 20 yr 12.7% Real risk-free rate Inflation premium Maturity risk premium Interest Rate Yield Curve can be Upward sloping, Downward sloping, or Flat

Forward rates Consider the following two investment alternatives for an investor who has a two-year investment horizon. Alternative 1: Buy a two-year zero-coupon instrument. (rate=s2) Alternative 2: Buy a one-year zero-coupon instrument (rate=s1) and when it matures in one year, buy another one-year instrument. Assume s1 8.000% s2 8.995% Note that: In a world of certainty (future interest rates are known) both of these strategies must yield identical final payoffs. Otherwise, no one holds either the two-year bond or the one year bond Given the price of zero-coupon bond, you can find the interest rate from the following formula Pk=$1000/(1+sk)k

Forward rates approximately (s1+f1,2)/2=s2 The interest rate that would need to prevail in the second year to make the short and long-term investments equally attractive, ignoring risk is called the forward rate. approximately (s1+f1,2)/2=s2 or exactly (1+s1)(1+f1,2)=(1+s2)2 when you know s1 and s2, you can calculate f1,2 f1,2=9.99% approximately or 10% exactly

Forward rates Now consider the case of uncertainty where future interest rates are uncertain. Assume that E(s12)=10% same as the forward rate P1-year=$1000/1.08=$925.93 P2-year= $1000/(1.08*1.1)=$841.75 So 2-year security is priced using E(s12). Note that this is consistent with the s2=8.995%, $1000/(1.08995)2=$841.75

Forward rates Consider a short-term investor who wishes to invest for one year Under Alternative 2:the return is a riskless 8% Under Alternative 1:the return is risky. If s12 turns out 10% as expected, the return will be 8% since the bond price will be $1000/1.1=$909.09 in one year and $841.75*(1.08)=$909.09. If s12 turns out different than 10%, the return will not be 8%. Why should this investor buy the risky 2-year bond when its expected return is 8%, no better than that of the risk-free one-year bond. This requires the 2-year bond to sell at a price lower than the $841.75

Forward rates Suppose all investors have short-term horizons and therefore are willing to hold the 2-year bond only if its price falls to $819. At this price, this year’s expected return on this bond is 11% ($909.09/$819=1.11). This means a premium of 3% compared to the risk-free one-year bond. In this environment, the forward rate f12 no longer equals E(s12). s2 now equals 10.5%((1000/819)1/2=1.105) and f12=13%. Investors require a premium to hold the two-year bond and be willing to hold the bond if E(s12) is less than f12. E(s12) < f12 means: since 2s2=s1+f1,2 then 2s2>s1+E(s1,2) The change in s2 by 1.5% (10.5%-8.995%) denotes a positive MRP. It is the risk premium given for holding long term bond.

Forward rates We can also imagine a scenario in which long-term bonds can be perceived by investors to be safer than short-term bonds. Suppose all investors have long-term horizons (2-year). In this case, investing in two-year bond is riskless and investing in one-year bond has reinvestment rate risk. This would cause E(s12) to be more than f12. In this case, we will have a negative MRP.

Term Structure Theories try to explain the shape of yield curve e.g. Pure Expectations Hypothesis The PEH argues that the shape of the yield curve depends on investor’s expectations about future short term interest rates. If short term interest rates are expected to increase, long-term rates will be higher than current short-term rates, and vice-versa. Thus, the yield curve can slope up, down, or even bow.

Assumptions of the PEH Assumes that the maturity risk premium for Treasury securities is zero. It states that f1,2 =E(s12). This implies that long-term rates are an average of current and expected future short-term rates. e.g. s2=[s1+E(s1,2)]/2 If PEH is correct, you can use the yield curve to “back out” expected future interest rates.

Pure Expectations Hypothesis Long-term rates are an average of current and expected future short-term rates. For example: s3=(s1+f12+f23)/3 To confirm definition of f12 s2=(s1+f12)/2  f12=2 s2-s1 definition of f23 s3=(2s2+f23)/3  f23=3 s3-2s2 Plug into the first expression s3=(s1+2 s2-s1+3 s3-2s2)/3= s3 PEH says s3=(s1+E(s12)+E(s23))/3 since E(s12)=f12 and E(s23)=f23

Pure Expectations Hypothesis Also note that: definition of f12 2 s2=(s1+f12)  f12=2 s2-s1 definition of f23 3s3=(2s2+f23)  f23=3 s3-2s2 definition of f13 3 s3=(s1+2f13)  2f13=3 s3-s1 Then f13=(f12+f23)/2

An example: Observed Treasury rates and the PEH Maturity Yield 1 year 6.0% 2 years 6.2% 3 years 6.4% 4 years 6.5% 5 years 6.5% Upward sloping yield curve If PEH holds, what does the market expect will be the interest rate on one-year securities, one year from now? Three-year securities, two years from now?

PEH says that one-year securities will yield 6.4%, one year from now. One-year forward rate 6.2% = (6.0% + x%) / 2 12.4% = 6.0% + x% 6.4% = x% PEH says that one-year securities will yield 6.4%, one year from now.

Three-year security, two years from now 6.5% = [2(6.2%) + 3(x%)] / 5 32.5% = 12.4% + 3(x%) 6.7% = x% PEH says that three-year securities will yield 6.7%, two years from now.

Calculating all the forward rates In the calculation above we relied on the expression E(s25)=f25 Equivalently, we can use the fact that long term rate is arithmetic average of short term rates s1 6.0% s2 6.2% f12 6.4% =2s2-s1 s3 f23 6.8% =3s3-2s2 s4 6.5% f34 =4s4-3s3 s5 f45 =5s5-4s4 three-year securities two years from now E(s25)=[E(s23)+E(s34)+E(s45)]/3=[6.8%+6.8%+6.5%]/3 =6.7%

Conclusions about PEH Some would argue that the MRP ≠ 0, and hence the PEH is incorrect. Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier. Thus, investors demand a MRP to get them to hold L-T securities (i.e., MRP > 0).

Conclusions about PEH recall that s2=(s1+f12)/2 If MRP≠0 and PEH is not correct Recall definitions of s1 and s2 s2=k*+IP2+MRP2 and s1=k*+IP1 assuming MRP1=0 E(s12)=k*+IP12 so IP2=(IP1+IP12)/2 s2=k*+(E(s12)-k*+s1-k*)/2+MRP2 since f12= 2s2 - s1 then f12= E(s12)+2MRP2

Conclusions about PEH f12= E(s12)+2MRP2 If yield curve is upward sloping i.e. s2>s1, then since 2s2=s1+f12 it must be f12>s1 If PEH is correct, then since f12= E(s12) it must be E(s12) >s1 If MRP≠0 and PEH is not correct, then we get E(s12)+2MRP2>s1 So it is not necessarily true that E(s12) >s1, i.e. it can be that E(s12) <s1 but E(s12)+2MRP2>s1

Example Assume that the real risk free rate is 3% and that inflation is expected to be 8% in year 1, 5% in year 2, and 4% thereafter. Assume that all treasury bonds are free of default risk. If 2-year and 5-year treasury bonds both yield 10%, what is the difference in maturity risk premiums on the two bonds?

Example Assuming that real risk free rate and MRP stay constant over time MRP5 = 10% - 8% = 2%. MRP2 = 10% - 9.5% = 0.5%. MRP5- MRP2 = (2% - 0.5%) = 1.5%.

Exact solution Exact solution : (1+3%+8%+MRP5)(1+3%+5%+MRP5)(1+3%+4%+MRP5) (1+3%+4%+MRP5)(1+3%+4%+MRP5)=(1+10%)5 MRP5=2.011% (1+3%+8%+MRP2) (1+3%+5%+MRP2)=(1+10%)2 MRP2=0.51%

Example 4-6 The real risk free rate is 3 percent. Inflation is expected to be 3 percent this year, 4 percent next year, and then 3.5 percent thereafter. The maturity risk premium is estimated to be 0.0005*(t-1), where t= number of years to maturity. What is the nominal interest rate on 7-year Treasury note? MRP1= 0.0005*(1-1)=0, MRP2= 0.0005*(2-1)=0.05% MRP7= 0.0005*(7-1)=0.3% IP7=(3%+4%+5*3.5%)/7=24.5%/7=3.5% S7=k*+IP7+MRP7=3%+3.5%+0.3%=6.8%

Example 4-12 The 5-year bonds on Cartwright Enterprises are yielding 7.75% per year. Treasury bonds with the same maturity are yielding 5.2 percent per year. The real risk free rate has not changed in recent years and is 2.3 percent. The average inflation premium is 2.5 percent, and the maturity risk premium takes the form: MRP=0.1%(t-1), where t= number of years to maturity. If the liquidity premium is 1 percent, what is the default risk premium on Cartwright’s corporate bonds? MRP5= 0.1%(5-1)=0.4% Treasury bonds: k*+IP5+ MRP5 =2.3%+2.5%+0.4%=5.2% Cartwright’s corporate bonds k*+IP5+ MRP5 +LP+DRP LP+DRP=7.75%-5.2%=2.55% so DRP=1.55%