CHAPTER 7 Want to Make a Trade? • Imagine I plan want to borrow some money from you today. I promise to pay you $1000 at the end of 5 years and I promise to pay you $50 per year for the next 5 years. • How much will you let me borrow? What is a bond? • Bond = • A struDon't forget about the age old question of Who is Tim Berners-Lee and what did he accomplish? Why?
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ctured way to borrow • Organized way for borrowing to happen • Every bond has a contract with its rules • Result of money being borrowed with the promise to repay • Bond contract specifies the details of the repayment • Bonds are usually long term (longer than one year) • A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond. ∙ 2 parties involved: ∙ Issuer = party borrowing money (bond is liability) ∙ Investor/bondholder = party loaning money (bond is asset) o Lender (the one loaning the money. They hold the bond) o They hold the contract Contract Details • Face value: The amount of the debt to be repaid at maturity (a future date) • Amount you get pay back at the end of the contract (bond is over) • “Par value” or “Nominal value” • Assume $1,000 (typical size of a bond) • Face value is 1000 unless stated otherwise • Maturity: the borrowing period length • How long you have to go until you get your money back (when bond expires) ∙ Coupon payments: Periodic interest payments to be made while the bond is outstanding ∙ Interest payment that are made on the way until the money is paid back in the end ∙ This is like paying interest payments ∙ Name came from physical coupons ∙ Typically happens once every 6 months or annually o Six month is more common ∙ Coupon rate x face value (for annual) ∙ For semi annual: same as above but divide by 2∙ Coupon rate: percentage of par value paid in coupon payments each year (expressed as an APR). Multiply by par value to get dollar payment of interest. o Quoted percentage o Expressed annually always on a per year basis(APR) o Use rate for coupon payment o Payment / face value (for annual bonds only) Valuing a Bond • A bond generates a stream of cash flows for its owner • Bond gives the bond holder a stream of cash flows • People in retirement are attracted to bonds because you get constant cash flow • Can be represented as a timeline • Can be valued just like any other asset by finding the present value of its cash flows ∙ 2 components to the bond’s cash flows: o Coupon payments are an annuity Payment you get every period ∙ Repayment of principal at maturity is a single cash flow o Amount you get when borrowing is over ∙ The present value of the cash flows represents the price of the bond What discount rate? • The coupon rate? no • WE NEVER USE THIS RATE • Only thing coupon rate is for is for the coupon payment (coupon rate, coupon payment) • No, because this is determined at the time the bond is issued and may or may not reflect current market conditions • Instead, we use a Market-Determined Discount Rate • Should reflect the risk of the cash flows • We’ll call it the “market rate” for now • Rate changes when market conditions change • MARKET RATE for Discounting Calculate the Value of a Bond • This bond has a $1,000 lump sum (the par value) due at maturity (t = 10), and annual $100 coupon payments beginning at t = 1 and continuing through t = 10. The price of the bond can be found by solving for the PV of these cash flows. Semiannual Bonds Review (3 adustments) 1. Multiply years by 2: Number of periods = 2N 2. Divide nominal rate by 2: Periodic rate (I/YR) = rd/23. Divide annual coupon by 2: PMT = Annual coupon/2 Example • A 3-year bond has a 6.5% coupon rate and makes payments semi-annually • Find the present value if the market rate (expressed as APR) is: • 3.95% • 6.5% • 10% Coupon and Market Rates • In general, how will the price of the bond vary with the market rate of interest? • Market Interest Rate = Coupon Rate • Price of bond = Face value • Market Rate > Coupon Rate • Price of bond < Face value • Sold at a Discount • Market Rate < Coupon Rate (Bondholders required return < Coupon rate) • Price of bond > Face value • Sold at a Premium • Required rate of return is the coupon rate • I: the % that the guy wants to earn (like “wants to earn a return of 11%) • PMT: the payment is the coupon rate x the par value Bond Yields • Bonds are traded in the markets, so price can be viewed as the market’s assessment of the present value of its cash flows • If asked for YTM then solve for I/Y • If you are a bond trader you figure out what bond is worth and then trade bonds based on that price • How much are we going to make • YTM: this is how much you are going to make • Yield-to-Maturity (YTM): Discount rate that equates bond price to the present value of all promised cash flows • When solving for price, we took the as given • When solving for YTM (discount rate), we now take the ____________________as given • YTM is yield promised to an investor who holds the bond until maturity (under certain assumptions) • If we know price is equal to par this means the yield (market rate) is = to coupon rate • If selling at discount then yield is bigger than coupon rate • If bond is selling at a premium then my yield is low Solving for the YTM• Solving for I/YR, the YTM of this bond is 10.91%. This bond sells at a discount, because YTM > coupon rate. 3/27/17 As Maturity Approaches ∙ Length of time until the bond is repaid is bond maturity • At maturity, the only cash flows for the bond are the par repayment and the final coupon o As maturity approaches, bond price will converge to par value ∙ Implications: o Premium bond price will decrease with time (premium is when bond is high/ above par value) Price is going to come down over time o Discount bond price will increase with time Current yield • Current yield = annual coupon divided by bond price • Tells me about how much money I’m making right now • For a discount bond, CY < YTM (YTM=Yields maturity) • For a premium bond, CY > YTM EXAMPLE • Find the current yield for a 10-year, 9% annual coupon bond that sells for $887, and has a face value of $1,000 • Current yield = 90/887 = .01015 = 10.15% Semiannual interest Payment • Corporate bonds typically pay interest to bondholders semiannually. • Corporate bond is a debt security issued by corporation that has promised future payments and a maturity date. • Borrowing publicly can be less expensive then borrowing from a bank • If the firm fails to pay the promised future payments of interest and principal, the bond trustee can classify the firm as insolvent and force the firm into bankruptcy. • If you invest in a corporate bond, you are lending money to the company and the company promises to make payment to you in a coupon payment and also pay you the money back What is the value of a 10-year, 10% semiannual coupon bond, if rd = 13%? 1. Multiply years by 2: N = 2 x 10 = 20 2. Divide nominal rate by 2: I/YR = 13/2 = 6.5 3. Divide annual coupon by 2: PMT = 100/2 = 50 Assignment #5 see page 239-241Selling a Bond Early • Recall that YTM is yield promised to an investor who holds the bond until maturity • You aren’t getting all the money for the life of that bond (don’t get yield of maturity) • Q: What if you sell the bond early? • Bond prices change when interest rates change • If you sell prior to maturity, calculate return based on price at which you sell the bond • Ex: Pay $1100 for a bond, hold for 6 months receive coupon payment of $50, then sell for $1150 Risks Faced by bond investor • Is bond investing risky? – YES! • 3 risks faced by bond investor: • Interest rate risk (price risk) – Risk associated with price fluctuations caused by interest rate changes • Reinvestment rate risk – Risk associated with the rate at which coupons are reinvested • Default risk (credit risk) – Risk associated with issuer’s ability to make payments as specified Interest Rate Risk • Price moves indirectly with interest rates • Longer-term bonds have greater interest rate risk • Most sensitive to these changes. Same with lower-coupon bonds • Lower-coupon bonds have greater interest rate risk • If a bond is held to maturity, interest rate risk is irrelevant • Investor is less concerned about interest rate risks Reinvestment Rate Risk • Reinvestment risk = risk that rd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income. • To earn the YTM, coupons must be reinvested at the same YTM. If this is not achieved, final yield will be different • YTM might be lower then thought • When interest rates are high, this is a problem • Move in opposite directions with interest rate risk • Note: Interest rate risk and reinvestment risk work in opposite directions Default risk • Worried that borrower is not going to pay • Default risk = Risk issuer won’t make payments as specified in the contract • Default = not paying the full amount • Default = not paying at the appropriate time • Bond rating agencies assess the default risk of borrowers• Bond rating agencies assess the default risk of borrowers • Risk score will determine what interest rate will be on your mortgage • Default premium = higher interest rate to compensate the bondholder for the risk of default • Go watch video over this subject Bond Ratings • Slide 32 • AAA is the highest • Can have plus and minus • + Means your closer to the next one • Cut off at BBB o Triple B and above is Investment grade (eligible for everyone to invest in Less regulation Old long stable firms More people can invest in you o Bellow this you are high yield or junk (there are limitations to who can invest in you) This is new firms or young There will be companies that are not allowed to invest in you Factors Affecting Default Risk and Bond Rating • Financial performance • How is this firm doing for they have a lot more debt • Debt ratio • TIE ratio • Current ratio (how much cash does the firm make) • Qualitative factors: Bond contract terms (ease concern of not getting money back to lenders) • Secured vs. unsecured debt • When you put up collateral if secured • Senior vs. subordinated debt • Senior: older debt • Subordinated: class bellow senior debt • Guarantee and sinking fund provisions • Debt maturity Special Cases • Zero-coupon bonds: Coupon rate of 0% • Par repayment is only cash flow • ALWAYS Sell at a discount • All else equal, have greater interest rate risk• Interest rates are more of a concern cause you don’t get coupon payment and price will move around a lot cause moving interest rate ∙ Floating-rate bonds: Coupon payments change over the bond’s life o Not fixed coupon payment Usually track a market interest rate (liber: rate in UK and a lot of these bonds will follow this rate) ∙ Rate typically indexed to some market rate ∙ Reduces interest rate risk o This is why companies like these o They move with interest rates o Follows interest rates so less worry that you aren’t getting a good rate when you sell ∙ Consol bonds: They pay interest forever and never mature. They are perpetuities o Never mature Bonds with Options Attached ∙ One party gets the ability to change the terms of the contract o Effects the interest rate (coupon rate) o If option is good for borrower then the borrower has to pay the investor for the option Kind of like reserving it Reserving a choice (I want to have this choice in the future) The one preserving that choice is the one who is having to pay I wanna reserve my right to choice in the future and I wanna reserve that. Who ever wants this will have to pay ∙ If choice is good for the borrower, the borrower has to pay the lender a higher interest rate ∙ If choice benefits lender, they are going to get a lower interest rate o They lock in a lower interest rate because they want flexability • Option gives one party the ability to change the terms of the contract • How does this affect the interest rate? • Option benefits the borrower…higher interest rate (borrower pays the attached option) • Option benefits the lender…lower interest rate (lender pays the attached option) • Questions 2-3 in homework; See page 224-228 in text Convertible Bond • Conversion option gives the bondholder (investor) the ability to convert the bond into a specified number of shares of the issuer’s stock • Often issued by young firms • Would do this If stock price increases, bondholder converts• If stock price doesn’t increase, bondholder does nothing ∙ Convertible bond will have a lower interest rate, all else equal (lender pays the attached option) ∙ Used a lot by young firms cause they experience a lot of stock growth ∙ All else equal, will have a lower interest rate ∙ Good for the investor/bondholder ∙ Lower interest rate for borrower because it is good for lender Callable Bond ∙ Is good for the firm (lets issuer pay off early ∙ Morgages ∙ If this is not in the contract then you cant pay it off early • Call option allows issuer to pay bond off early at a pre-specified price and time (call it in) • Call price typically greater than par • Call period is typically later in the bond’s life • If interest rates go down, issuer can call the bonds in and then re-issue at a lower rate • Yield-to-call (YTC) = yield calculation that assumes bond will be called in • Call price serves as a ceiling for the market price of the bond (if you want to pay it off early, you pay the call price) o Callable bonds will have a higher interest rate, all else equal (borrower pays the attached option) o If interest rates go down, then a firm will want to do this (Company calls in old debt with high interest rates and issue low interest rate) (if you are investor, you are going to get the yield to call. You only make money until the firm calls it back) o Call provisions (page 226) Puttable bond ∙ Gives the choice to the investor (they can sell it back early) ∙ Good for investor • Put option allows bondholder to sell bond to issuer early at a pre-specified price and time • Put price typically lower than par • Amount you get back is less than 1000 • Want this when interest rates goes up • Put period is typically later in the bond’s life • If interest rates go up, bondholder can sell the bonds to borrower and then re-buy at a higher rate • Yield-to-put (YTP) = yield calculation that assumes bond option will be exercised (not on test) • Put price serves as a floor for the market price of the bond• EX: You are a lender and you lend the money at a low interest rate. Now the interest rate is higher and you want to get your money back so that you can invest it at a higher interest rate • This will pay them more money • This bond isn’t paying a lot so let me trade it in and get something that pays more • Puttable bonds will have a lower interest rate, all else equal (lender pays the attached option) *** • Less common bond Summary: Four Key relationships • First Relationship The value of bond is inversely related to changes in the yield to maturity. (Price and yield to maturity) • Value of bond is high the yield to maturity is low • When one goes up then the other has to go down • When the yield to maturity is higher, the value of the bond is lower • When the yield to maturity is lower, the value of the bond is higher • Second Relationship: • Discount bond: if the market’s required yield to maturity is above the coupon interest rate then the market value of a bond will be less than the par value • Can compare coupon rate with yield • Premium bond: if the market’s required yield to maturity is below the coupon interest rate then the market value of a bond will be greater than the par value • Third Relationship As the maturity date approaches, the market value of a bond approaches its par value. • That’s because at maturity the bond will be taken away and the investor will receive the par value of the bond. Fourth Relationship Long term bonds have greater interest-rate risk than short-term bonds. • Interest rate and risk really atters and interest rate dictate if you are going to exercise an option in the bonds • While all bonds are affected by a change in interest rates, the prices of longer term bonds fluctuate more when interest rates change than do the prices of shorter-term bonds Chapter 7 Review • Key terms: • Bond; corporate bond; treasury bond; municipal bond; foreign bond • Municipal bond: issuer is a local government of the state • If investor is a resident of the issuing state, Interest earned on this bond is exempt from federal and state taxes • Contract terms: par value; face value; coupon rate; coupon payment; maturity• Callable bond; puttable bond; convertible bond • Discount bond; premium bond • Current yield; yield to maturity; bond price • Reinvestment rate risk; default risk; interest rate risk • Zero-coupon bond; fixed-rate bond • Investment grade bond; junk bond; bond ratings Chapter 7: Procatice problems page 258: (7-1,7-3,7-8,7-9,7-10) Integrated case 7-20 (page 261) YTM (annual semiannual Value of bond (annual; semiannual) Current yield; total return; capital gains yield Yield to call • Reinvestment rate risk is greater for high coupon bonds with short maturities. • All else equal Reinvestment rate risk is greater for bonds with higher coupon • The value of a bond decreases with an increase in interest rates • Bonds with long term maturities face higher interest rate risk Chapter 8 Calculating the Realized Return from an Investment • Realized return or cash return measures the gain or loss on an investment. • What you actually get (the money you actually make) • Gain or loss on an investment that actually happens • Example: You invested in 1 share of Apple (AAPL) for $95 and sold a year later for $200. The company did not pay any dividend during that period. What will be the cash return on this investment? • This means you buy for $95 and sell for $200 • Cash Return = Ending Price + Cash Distribution (Dividends) – Beginning Price • For Example Above: 200 + 0 (What you get on your investment while you are holding it) – 95 = 105 • We can also calculate the rate of return as a percentage. It is simply the cash return divided by the beginning stock price. • Percentage take into account that stocks have different starting points • Realized return: percentage you make on an investment • Rate of Return = Cash Return / Beginning Price = (Ending Price + Cash Distribution (Dividends) – Beginning Price)/ Beginning Price • EXAMPLE above: (200 +0 -95) / 95 = 110.53% (it over doubled) • EXAMPLE: Compute the rate of return for the previous example Intuition • Investors prefer dollars today to dollars in the future (Time preferences) • Rather consume (or invest) now than later• Suggests discount rate should be positive ∙ Investors don’t like risk (risk aversion) ∙ They require compensation for taking risks in the form of a higher expected return ∙ Also suggests a positive discount rate What is Risk? • Risk loosely refers to dispersion in possible outcomes (some better than others) • No dispersion (all outcomes are the same) = no risk (receive the same percentage return no matter what) • Greater dispersion (more variety of outcomes) = greater risk ∙ Consider a histogram (plot risk) ∙ More concentrated points = more safe ∙ Plots probabilities of all possible outcomes ∙ Represents a picture of the dispersion in outcomes ∙ Wider distribution = More risk ∙ In slide 9: This asset has no risk (Asset A) ∙ In Slide 10: half the time pays 7% and a quarter of the time it pays -1% and 15% Measuring Risk • Variance = average squared deviation from the mean (How things are distanced away from the average) • Think of dispersion (how are these things dispersed over outcomes?) • Represents the dispersion of a given distribution • Variance is a natural measure of risk ∙ Standard deviation = square root of variance o Higher standard deviation = higher dispersion = higher risk o Standard deviation measures risk (related to dispersion of the histogram) ∙ More commonly used to quantify risk. • Higher variance (or standard deviation) represents greater dispersion and, hence, greater risk Expected payout of a Coin Toss • Consider the toss of a fair coin. There is a 50% chance the coin lands on heads and there is a 50% chance the coin lands on tails. • If the coin lands on heads you win $10 • If the coin lands on tails you win $0 • What is the expected return? • Take weighted averageExpected Return • Expected return is the rate of return that the investor expects to earn from an investment in the future. • Measure of what you expect to have happen but is not what actually happens or might happen • It is the weighted average of the possible returns, where the weights are determined by the probability that it occurs. Why is the T-bill return independent of the economy? Do T-bills promise a completely risk-free return? • T-bills will return the promised 3.0%, regardless of the economy. • No, T-bills do not provide a completely risk-free return, as they are still exposed to inflation. Although, very little unexpected inflation is likely to occur over such a short period of time. • T-bills are also risky in terms of reinvestment risk. • T-bills are risk-free in the default sense of the word. • Outcome of financial research from the 70s Coefficient of Variation (CV) • A standardized measure of dispersion about the expected value, that shows the risk per unit of return. • CV= Standard Deviation / Expected return Standard Deviation for Each Investment (taking into account risk) ∙ σHT = 20% σUSR = 18.8% ∙ σM = 15.2% σColl = 11.2% ∙ This example is for T-Bills (below example) N σ = ∑ − (r rˆ) P 2 i i 1 = σ = T-bills σ = T-bills 1/2 ⎢⎢⎢⎣⎡+ − ⎥⎥⎥⎦⎤ 2 2 (3.0 3.0) (0.1) (3.0 3.0) (0.2) − + − 2 2 (3.0 3.0) (0.4) (3.0 3.0) (0.2) − + − 2 (3.0 3.0) (0.1) 0.0% Coefficient of Variation (CV)• A standardized measure of dispersion about the expected value, that shows the risk per unit of return. • Measure of desperation and expected value • Risk per unit of return • Standardize our risk and show us how much we make when we take that risk • To get 1% of return how much risk do I need to take? CV =Standard deviation Expected return =σr^ • • Can rank stocks by: how much risk you are taking to get the money Risk and Return of Different Assets ∙ In order to make money you have to take some risk • Consider stocks, long-term T-Bonds, and T-Bills • Which do you expect to be riskier? Why? • Long term bonds • Because they are long in nature (maturity risk), and T Bills are risk free • Since there is more risk then you have higher expected return • Which should have higher expected returns? ∙ What about different common stocks? ∙ Firms in hi-tech industry are riskier than firms in utilities industry? Why? ∙ Utility is stable cause very regulated by government (regular and consistent) ∙ High tech: like snap chat or Facebook ∙ High tech is riskier ∙ When there are more possible outcomes then it is riskier ∙ Immerging market is risker then United States economy Portfolio Construction: Risk and Return ∙ Not going to invest in one stock or one of anything ∙ Portfolio of all the stuff that they hold ∙ Think of the risk as everything as a group and not individually ∙ What we care about is the spill over o How it spills over or related to other components in my “basket” ∙ Take each of the pieces in the basket and weight them • A portfolio’s expected return is a weighted average of the returns of the portfolio’s component assets. • Standard deviation is a little more tricky and requires that a new probability distribution for the portfolio returns be constructed.Calculating Portfolio Expected Return ∙ Assume a two-stock portfolio is created with $50,000 invested in both High Tech and Collections. ∙ Start with portfolio with 100,000. With 50,000 invested in high tech and 50,000 in collections o First thing to figure out: weight on each asset (W) (% in each asset that goes to the portfolio) 50% in high tech and 50% in collections o ∙r^p is a weighted average: N r^p=∑ ∙ i=1 wir^i ∙r^p=0. 5(9. 9 )+0 .5(1. 2 )=5.5 ∙ Portfolio risk: expected return – return we get from each state of the portfolio Diversification • Which will have a higher standard deviation – an individual asset or a portfolio of assets? • Individual asset • Because if this one thing does bad, there is nothing to off set it • Assume returns of different assets are not perfectly correlated (how two things move together) • We want gains in one part are off set by losses in another part • Reduces risk because if one thing is bad the other is doing good • Gains in some of the portfolio’s assets will offset losses in other assets • End result: Return variability (standard deviation) is reduced when assets are combined in a portfolio ∙ Diversification = a strategy designed to reduce risk by spreading a portfolio across many assets o Instead of just investing in one thing, invest in something else and now you have spread your wealth across different assets and now you reduce your risk o Holding diverse set of things o Holding things that look different from each other Can hold lots of things that look the same o More variety: more diversification benefit (less risk) ∙ Correlation Coefficient Range • -1.0 (perfect negative correlation) • Meaning that two variables move in perfectly opposite directions to each other (one goes down and ones goes up • Never in the same direction • +1.0 (perfect positive correlation) • Meaning that two variables move perfectly in the same direction • Stuff in same industry tend to move together • Lower the correlation, Greater will be the diversification benefits • Want lowest correlation that you can get (the closest it is to -1) • Correlation has to be between -1 and 1 • More stocks you hold, the less risk you take • In the graph: • Light blue area is the part of risk that you cant • Dark blue part we can reduce Breaking Down Sources of Risk ∙ Stand-alone risk = Market risk + Diversification risk o Market Risk: risk that is in the stock market its self Related to how the economy is doing (what interest rates look like) o Market risk: portion of a security’s stand-alone risk that cannot be eliminated through diversification. • Measured by beta. • Tells us how much market risk there is • How much of this risk can I not get rid of • Aka. Systematic Risk (risk in the system) • Diversifiable risk: portion of a security’s stand-alone risk that can be eliminated through proper diversification. • Aka. Firm-specific risk (risk that is particular to that specific firm) • Aka. Idiosyncratic risk (Individual source of risk) • Assignment # 3 & 4 (page 275 – 281) A Simple Model • Systematic risk (market risk) is exposure to price shocks that are common to all assets • All stocks have some risk that effects everyone • Think macroeconomic news events (systematic risk) • Different assets may be affected differently, but all are affected • Some stocks might be more sensitive than others • Want to measure how sensitive a stock is to what is happening systematically • Common price shocks are captured by the market portfolio • An asset’s systematic risk is described by its sensitivity to the market portfolio (Beta) • In finance we cant use beta for anything else. Only ever called beta • Sensitivity of a stock to the market Comments on Beta • Beta measures sensitivity to the market • Measures a stock’s market risk (sensitivity to market)• If beta = 1.0 (the security is just as risky as the average stock.) • This stock has average market risk • What ever happens to the market as a whole will exactly happen to this stock • If beta > 1.0 (the security is riskier than average) • This stock is risker than what is going on in the market on average • Risker side of market • Small movement in market, this stock moves a lot • Moves on the extreme • If beta < 1.0 (the security is less risky than average) • Move in the market, this stock doesn’t move very much • Insulated relative to the market • Most stocks have betas in the range of 0.5 to 1.5. • Most are around the average market stock The Security Market Line (SML): Calculating Required Rates of Return • Where the beta comes from • SML is the required rate of return • Ri= return of the stock (one of the pieces you will be solving for) (required rate of return, how much you need to get into that stock) o Required rate of return: given the level of risk involved this is how much I have to get paid in order to invest in the stock The amount investors require back Will not invest in this stock unless they think they are going to get this back How much they require given the risk involved Treasury bill is the starting point SML: ri = rRF + (rM – rRF)bi ri = rRF + (RPM)bi • bi = beta • RPM is market risk premium o Market return – risk free rate (rM – rRF • Assume the yield curve is flat and that rRF = 3.0% and • RPM = rM – rRF = 8% - 3% = 5% • **ON exam: if give Market risk premium (already subtracted the Risk free rate) • If given the market return: and the risk free return then you need to calculate the Market risk premium • How im compensated for every unit of risk I take above and beyond the risk free rate What is the Market Risk Premium? • Amount you need above risk free rate • The more investors don’t like risk, the more you have to pay in order for them to risk (lots of promises) • Additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk. • Its size depends on the perceived risk of the stock market and investors’ degree of risk aversion. • Varies from year to year, but most estimates suggest that it ranges between 4% and 8% per year. (above the risk free rate) Slide 37: • First row: what your expecting to make • Second row: required rate of return. o How much you have to be paid in order to invest and based on the risk o Over valued Required return > expected return o Undervalued Required return < Expected return Want to buy these rˆ r High Tech 9.9% 9.55% Undervalued Market 8.0 8.00 Fairly valued US Rubber 7.3 7.40 Over valued T-bills 3.0 3.00 Fairly valued Collections 1.2 0.50 Under valuedAn Example: Equally-Weighted Two-Stock Portfolio • Create a portfolio with 50% invested in High Tech and 50% invested in Collections. • The beta of a portfolio is the weighted average of each of the stock’s betas. bP = wHTbHT + wCollbColl bP = 0.5(1.31) + 0.5(-0.50) bP = 0.405 (beta of whole portfolio)Calculating Portfolio Required Returns • The required return of a portfolio is the weighted average of each of the stock’s required returns. rP = wHTrHT + wCollrColl rP = 0.5(9.55%) + 0.50(0.50%) rP = 5.0% o 9.55 is from Security market line (this is what I require from the risk) o Assignment # 5 &6 PG: 275-286 • Or, using the portfolio’s beta, CAPM can be used to solve for the portfolio’s required return. rP = rRF + (RPM)bP rP = 3.0%+ (5.0%)(0.405) rP = 5.0% CHAPTER 8 Review • Key terms • Risk; stand-alone risk; market risk; standard deviation; correlation; coefficient of variation; beta; systematic risk; diversifiable risk • Expected return; portfolio expected return; required rate of return; realized rate of return • Risk premium; market risk premium; • Capital asset pricing model; security market line (figures out the required rate of return • The systematic risk component measures the contribution of the investment to the risk of the market portfolio. • Risk within the market • War, recession. • Risk in the system • Happening in the market as a whole • The unsystematic risk is the element of risk that does not contribute to the risk of the market and is diversified away. • Diversifiable risk • Risk you can get rid off • Product recall, labor strike, change of management. • Risk you can get rid of that is specific to a company • Effect just one firm • The straight line relationship between the betas and expected returns is called the security market line (SML), and its slope is often referred to as the reward to risk ratio. • Risk reward ratio • More market risk an investment the higher the beta. The more you expect to return and the higher the expected returns • The higher the systematic risk of an investment, other things remaining the same, the higher will be the expected rate of return an investor would require to invest in the asset. • PRACTICE PROBLEMS • 8-1, 8-2, 8-3, 8-5, 8-6, 8-10, 8-1 CHAPTER 9 Common stock • Common stockholders are the owners of the firm. They elect the firm’s board of directors who in turn appoint the firm’s top management team. The firm’s management team then carries out the day-to-day management of the firm. • Owners of the firm (Holding these means you are a partial chapter) • These elect the board of directors • In charge of making major decisions that effect shareholders • These people Hire the CEO • Firm goes public and wants to earn money so they issue common stock • Trading publicly (you and I can invest in it) Voting Rights • Common shareholders are the only security holders given the right to vote. • Shareholders are the ones who vote • Most shareholders vote by proxy • This means they don’t actually vote but want to vote what ever CEO wants vote (or someone else just says who they side with) • Classified stock • Classes of common shares of stock • Class A and Class B • Different classes have different voting rights • Founders’ shares • Dual class share structure • Like Facebook: the owner still has private shares but they gave out public shares to raise money • See a lot with founding families • Passing down from generation • Tend to be more interested in long-term value • Take more risk • The owner still owns a lot of their company but has public owners • Special voting rights (when you are the main owner (dual class share structure) then your vote is pretty much the only one that matters) • Pages: 310-312 • Assignment #1 and 2 Investor Value example • You currently own 1,000 shares of stock worth $35 per share. The company has 18,000 shares outstanding. • What is the current market value of your investment? • (price*number of shares owned) • = $35,000 • What is the company’s total market value? • (price*number of shares outstanding) • = 35 * 18,000 • = $630,000 • Suppose the company will issue 2,000 more shares at $30 per share • What is the new value of the stock to you? What is the new value of the investment? • New market value= o Existing share price * existing shares + New price * new share ∙ New share value= o New market value/total outstanding shares ∙ New investment value= o New share value * # of shares Pre-emptive right • Gives investor the right to buy newly issued shares to maintain the same percentage of ownership • Example, you owe 5.56% of the firm, so you can buy 5.56% of new shares (111 shares) • New investment value = Existing price * existing shares + New price * new shares How to value common stock • Intrinsic value • Not something you can observe or measure but you can estimate it • Fundamental value • Value based on expected future cash flows and risks involved • Market price • Value perceived by stock market investors • Equilibrium • When the intrinsic value equals the market value • If we are not in equilibrium then there will be trading happened • Traders try to buy these miss priced stocks • If the intrinsic value is less than the market price, investors sell • If intrinsic value is more than the market price, investor buy • If intrinsic value is less than market price they sell if its more than market price then they buy How to estimate intrinsic value (how we estimate actual value of stock) • Discounted dividend model• Based on present value of future dividends • Based on how a firm pays out to shareholders • Corporate valuation model • Done a lot in practice • Based on money the company brings in • Values the company • Useful cause not all firms pay dividends • Useful if they don’t pay them • When a firm does not pay dividends • Based on value of free cash flow 4-6-17 Dividend Discount Model ∙ If a firms cash dividends grow by a constant rate, then the common stock can be valued as a perpetuity ∙ Assuming dividends grow at a constant rate ∙ Dividend: when a stock brings in money and they have extra earnings then they pay that money to the shareholders o Profit sharing with the owners ∙ Value = Dividend in period 1/(required rate of return – dividend growth rate) o IN PERIOD 1 NOT 0 o Required rate of return! Output of the Security market line ∙ Will tell us the estimate of the intrinsic value of stock Required rate of return • Investor’s required rate of return is determined by two key factors: • The level of interest rates in the economy • The risk of the firm’s stock (This is beta) • If these two increase then we are going to have a higher required rate of return • If interest rates rise of the level of risk increases, the required rate of return increases • Use the Security Market Line (SML) to calculate the required rate of return • If the risk free rate is 3%, the return on the market is 8% and beta is 1.2, what is the required rate of return on the firm’s stock? = 3% + 1.2*(8% - 3%) = 9% Growth rate • There are two key determinants for the growth rate of future dividends • The return on equity (ROE)• How much the firm earns when it reinvests earnings back in the firm • When the firm reinvests its earnings how much return do we get on that • How well does the firm generate more money with the money it has • If the ROE is high the growth rate should go up • The retention ratio • The amount of firm’s earnings that are reinvested in the firm • How much does the firm put money back into the firm • How much of the firms earnings are reinvested • The more you put back into the firm, the faster it will grow Model Assumptions • Dividends grow at a constant rate to infinity • Assume once a firm starts paying dividends then it always pays till infinity • The growth rate must be less than the required rate of return • Otherwise the denominator would be 0 or (-) • The model can be used for negative growth and no growth stocks • If G is 0 then it’s a no growth stock • If firm is shrinking then the G is negative Dividend discount Model Example • What is the value of a share of common stock that paid $6 dividend at the end of last year and is expected to pay a cash dividend every year from now to infinity, with that dividend growing at a rate of 5 percent per year, if the investors required rate of return is 12% on that stock? • Steps: • Calculate Dividends in period 1 • Use the formula Example Continued • What is the expected stock price one year from now? • Expected P1 = P0(1+g)