Chapter 5: Intro to Risk and Return 5.1 Risk-Return Relationship Risk Determined by the uncertainty of future cash flows This uncertainty is the result of factors peculiar to each asset Portfolio of Assets A collection or group of assets Modern Portfolio Theory The theory that all investors hold a portfolio of assets called the market portfolio and that risk is measured by the correlation of an asset to this portfolio. The relationship between risk and return is captured by the CAPM equation WATCH EXPLAIN IT VIDEOS 5.2 Computing the Return on a Single Asset Computing Single Returns Holding period return (HPR) The return earned on an investment since its inception, not annualized Can separate equation into two parts, the first being capital gain and the second being dividend yield Average vs. Compound Average Arithmetic average return The return calculated where compounding is ignored Geometric (compound) average return The return computed that recognizes that interest or earnings are paid on accumulated interest or earnings. It is also called compound return The average is the sum of the returns in the sample divided by the size of sample (n) The compound average return is Computing Expected Returns Random Variables Variables with no identifiable relationship between each other Also known as states of nature Expected Return The return that is expected to be earned each period on a given asset 5.3 Evaluating the Risk of Holding a Single Asset Standard Deviation A popular statistical measure that quantifies the dispersion around the expected value Chapter 7: Interest Rates and Bonds 7.1 Zero Coupon Bond Features and Markets Zero Coupon Bond - A bond that does not pay coupons Short-maturity (less than 1 year) zero coupon bonds are traded on the money market - Buyers on the money market securities include pension funds and mutual funds. - Bankers’ acceptance o A short-term, unsecured debt instrument issued by a nonfinancial corporation but guaranteed by its bank. - Commercial paper o A short-term, unsecured promissory note issued by a corporation that has a very high credit standing, having a yield above that paid on U.S. Treasury issues and comparable to that available on negotiable CD’s with similar maturities - T-bills o Bonds issued by the U.S. government that have maturities of 91, 182 days or 52 weeks. 7.2 Zero Coupon Bond Yields and Pricing Solving for the return (yield to maturity) The Term Structure of Rates and the Yield Curve - The relationship between term (maturity date) and interest rates The Yield Curve - A graphical representation of the term structure. A graph of yields on the y-axis against time to maturity (term) on the x-axis Treasury Spot Rate Yield Curve - A graph showing the yields on U.S. government zero-coupon bonds on the y-axis against their time to maturity (term) on the x-axis Zero Coupon Bond Pricing The Inverse Relationship Between Bond Prices and Yields - If yields rise, then bond prices fall 7.3 Determinants of the Shape of the Yield - Downward sloping curve is called an inverted yield curve Five Factors that determine the position and shape of the spot rate yield curve 1. Real interest rates 2. Inflation 3. Maturity preference 4. Default risk 5. Liquidity Interest Rates and Inflation - Interest rates include a component to compensate lenders for inflation. Inflation drives a wedge between the real rate of interest, the rate that would prevail if there was no inflation, and the nominal rate of interest which is the observed rate. - In inflation = 0, then real = nominal Fischer Equation - The relationship between real and nominal Simplified: Ex. Real rate is 10% and inflation is 5%, then what is the nominal rate? The nominal rate is 15.5%. Expectation Theory - Long-term bond yields are the geometric average of the expected intermediate bond yields - Two investment strategies o Buy a 2-year bond with a yield of k2 per annum (lock in) o Buy a 1-year bond with a yield of k1 and roll over the investment into another 1year bond (roll over) - Expectations about future interest rates are largely based on expectations of inflation and monetary policy Maturity Preference Theory - Assumes that investors prefer short maturities and so like to roll over rather than lock in, to compensate borrowers must provide investors with higher yields to induce them to buy longer-term bonds, Maturity Risk Premium (MRP) - The premium incorporated in long-term bond yields to compensate investors who prefer shorter maturities - Derived from investors attitudes of two types of risk o Interest rate risk The risk of a capital loss on a bond investment. If interest rates rise, then bond prices fall. For an investor who has to sell a bond before maturity, an interest rate increase will cause a capital loss Lock-in strategy is at risk o Reinvestment rate risk The risk that rates in the future will fall and thus reduce the FV of a bond investment. Bond strategies that involve a sequence of short-term investments or coupon bonds that pay large coupons are both subject to reinvestment rate risk Roll over strategy is at risk WATCH EXPLAIN IT 7.3.3 Default Risk - Failure to fulfill an obligation o Failure of the borrower to make interest or principal payments or to follow the terms of the loan. - Default o Indenture An agreement with between the issuer of a bond and the bondholders that specifies the rights and obligations of the two parties o Covenants Covenants are conditions that the issuer must meet. Covenants include such things as maximum debt-to-equity ratios, minimum working capital levels, restrictions on dividend policy and capital expenditures, reporting requirements, and any other conditions the lender feels will increase the probability of timely repayment. If the borrower fails to keep any of the covenants, then the lender has the right to declare the borrower in default and to demand immediate repayment o Trustee Covenants are conditions that the issuer must meet. Covenants include such things as maximum debt-to-equity ratios, minimum working capital levels, restrictions on dividend policy and capital expenditures, reporting requirements, and any other conditions the lender feels will increase the probability of timely repayment. If the borrower fails to keep any of the covenants, then the lender has the right to declare the borrower in default and to demand immediate repayment o Collateral Assets pledged as security for the loan. If the borrower defaults, then the collateral is sold and the proceeds are used to satisfy any remaining obligations of the borrower. o Secured Bond Assets pledged as security for the loan. If the borrower defaults, then the collateral is sold and the proceeds are used to satisfy any remaining obligations of the borrower. o Mortgage Bond Secured with land o Debenture Unsecured bonds o Ratings Assets pledged as security for the loan. If the borrower defaults, then the collateral is sold and the proceeds are used to satisfy any remaining obligations of the borrower. o Ratings Agencies Debt rating agencies, such as Standard & Poor's and Moody's, rate the debt offered by firms. Bond ratings help investors predict the probability of default. Higher ratings (i.e., AAA) correspond with a low probability of default and lower ratings (i.e., CCC) indicate a higher probability of default. The ratings agencies use proprietary algorithms to estimate default probabilities based on accounting data. o Investment Grade A term used to refer to bonds from issuers with a rating of BBB (Baa) or higher. o Junk Bonds with a grade of BB (Ba) or lower Default Risk Premium (DRP) - A component of a bond yield that compensates the bondholder for the possibility that the issuer might default Liquidity - A securities market with a high volume of trading activity in which it is easy to buy and sell. Liquid markets also have depth, which means large quantities can be traded quickly without impacting the price adversely. Liquidity Risk Premium - A component of a bond yield that compensates the bondholder for the potential costs in selling the bond Reconciling the Theories - Yield to Maturity = + INF + MRP + LRP + DRP o = the real rate of return on an inequivalent (default-free) government bond o INF = inflation premium from Fischer equation o Pi = the expected rate of inflation 7.4 Coupon Bond Features and Markets Coupon Bond - A debt instrument that pays periodic (annual or semi-annual) interest payments to the holder (called coupons) and pay a final lump sum (FV) at maturity. Coupon bonds are issued by governments and corporations. Coupon Bonds can also have several other features 1. Convertible bond o Allows holder of the bond to convert the face amount into a fixed number of common shares at any time before the maturity of the bond if they so choose 2. Callable Bond o One where the issuer has the right to force early redemption of the bond (before the maturity date). When a bond is called, the holder must return the bond to the issuer. In exchange, the issuer paus the holder the face value of the bond. In some cases, the holder may receive a call premium, which is a small payment to compensate over the inconvenience of the call. 3. Foreign Bond o Bond that is issued in a particular country and is denominated in that country’s currency. 4. Variable coupon is called a floating rate bond Coupon Bond Markets - The bond market is the market for coupon and zero-coupon bonds with maturities ranging from 1 to 30 years and includes bonds issued by government and corporations. - Both money market and bond market are over-the-counter and dealer markets, this means there is no centralized physical or computerized exchanges for bonds. They are done privately and negotiated through multiple dealers or market makers, such as banks and large brokerages. Bond Price Reporting - Issuer: U.S. Government - Coupon Rate = annual coupon divided by face value - Price, two-part price quote. Handles and “32nds“ - Yield = YTM 7.5 Coupon Bond Yields and Pricing Ex. A 1-year zero coupon bond has a face value of $C, where $C=$10. A 2-year zero coupon bond has a face value of ($C + $FV), where $C=$10 and FV=$100. What are the prices of the bonds if the 1-year spot rate is 1% (k1=1%) and the 2-year spot rate is 2% (k2=2%) ? = 115.63 Law of One Price - If two investments with identical characteristics (e.g. cash flows, maturity and risk) trade in two different markets, then the investments must trade for the same price For any number of coupons, n, we can express the price of a coupon bond as follows: Yield to Maturity Calculate the YTM Ex. A 2-year coupon bond has a coupon rate of 5% and a FV of $1000. The price of the bond is $1038.75. What is the yield-to-maturity of the bond? Some insights about YTM 1. YTM is approx. equal to the return that the bond holder will earn is they pay the price and holds the bond to maturity 2. YTM calculation implicitly assumes that intermediate coupons can be reinvested at the solution rate. If the bond holder’s reinvestment rate differs, then her actual return will not equal the YTM. 3. YTM can only be calculated if the bond price is known. The yield is thus interchangeable with the price. In other words, we are given the price, then we can solve for the YTM. Vice-versa. Bond Valuation with Annual Coupons Ex. Suppose you found a bond in your aunt’s attic. It has 2 years before it matures (it has been in that shoe box for 28 years now), a 10% coupon rate, and a $1,000 face value. If interest is paid annually and the yield to maturity of the bond is 9%, then what is the current price of this bond? Ans. Semi-Annual Coupon Bonds 1. Divide the annual coupon payment by two. C/2 2. Discount semi-annual coupons with the semi-annual yield. Kd/2 3. Double number of periods Ex. The bonds have a 10.95% coupon rate that is paid semi-annually, a $1000 FV, and matures in 20 years. YTM = 12% Step 1: Calculate semi-annual coupon amount: Annual Coupon = C = 0.1095 X $1000 = $109.50 Semi-annual Coupon = Annual Coupon/2 = C/2 = $109.50/2 = $54.75 Step 2: Calculate semi-annual YTM YTM = kd = 12% Semi-annual YTM = kd/2 = 12%/2 = 6% Step 3: Solve with Pbond formula 7.6 Coupon Bond Yields and Pricing Premiums and Discounts - Premium o An expression used to refer to a coupon bond that trades for a price that is more than its face value - Discount o An expression used to refer to a coupon bond that trades for a price that is less than its face value - Par o Synonym for face value Longer Maturity Bonds Have More Interest Rate Risk - Longer bonds have more interest rate risk Bond portfolio managers take advantage of this bond pricing strategy by using interest rate expectation - A bond portfolio management strategy predicted on the successful prediction of future interest rates. It involves increasing a portfolio’s average maturity if interest rates are expected to fall and reducing it if interest rates are expected to rise. Capital Gains, Coupon Yields, and the YTM FINSIH 7.6 Chapter 8: Stock Valuation 8.1 Features of Stocks and Stock Markets 8.1.1 What is a Stock Stocks (Shares) - A security that represents ownership in an incorporated company Public Company - Shares are traded on the stock exchange, TSX, NYSX, Nasdaq, etc. Private Company - Shares are held by a relatively small number of individuals Common Shares - Principal way the corporations raise equity or capital, give owner one vote per share - Designated by classes, A, B, C, D and so on. - Stockholders are entitled to what is left after all obligations have been met, makes them residual claimants of the firm - Receive liquidation value, which is the value the firm will bring after subtracting all liabilities owed - Profits are distributed in two basic ways o Dividends o Stock repurchases Preferred Shares - Hybrid instrument because it has the characteristics of both common stock and bond - Pays a fixed amount, dividends - Do not have voting rights - Bond interest payments are paid before preferred dividends, but preferred dividends are paid before common - Preferred stock has culminative dividends, which means the BOD can suspend dividends and pay once BOD has unfroze the dividends - Entitled to par value 8.1.2 Stock Markets Primary Market - Market for newly appointed shares - IPO (initial public offering), occurs on primary market and goes to secondary market after - Seasoned offering is issuing shares that have been already traded 8.1.3 Trading Stocks Positions: Long and Short - Long o An investment where ownership is taken before the security is sold. This is the usual form investments take. - Short o The investor initially borrows the security. It is then sold. Later security is bought back to repay the loan Orders: Market and Limit - Market o Order to buy or sell that is to be executed as soon as possible at the best price obtainable - Limit order o A conditional order to buy or sell a security where it is only filled if the sell price is above a given level or the buy price is below a given level - Margin o The amount of money the investor must provide to purchase a security. The balance is supplied by the broker. The minimum margin in 50%. 8.2 Valuation of Preferred Stock Formula for the PV of a perpetuity Ex. If investors require 12.5% return, and the stock pays an annual end-of-year dividend of $1.50, what is the market price per share? 8.3 The Valuation of Common Stock Using the Dividend Discount Model 8.3.1 The One-Period Valuation Model Ex. Find the price of the Intel stock given the figures reported on the previous page. You will need to know the required return of stockholders to find the present value of the cash flows. Assume that you would be satisfied to earn 12% on the stock. 8.3.2 The Generalized Dividend Valuation Model The Generalized Dividend Valuation Model A model used to compute the value of stock that assumes its price is the present value of all future cash flows The Constant Growth Model Simplified This model is useful for finding the value of stock under two chief assumptions: 1. The growth is constant forever o Dividends are assumed to continue growing at a constant rate forever 2. k > g o The growth rate is assumed to be less than the required return on equity Stock Market Volatility Computing the Required Return on Stock - Rearranging the constant growth model to solve for k: k - High yield stocks pay out a large portion of their net earnings as dividends Zero or low yield stock retain all or most of their earnings and reinvest them in the company Dividend Yield - The ratio of the dividends paid in a year divided by the current price Nonconstant Growth Model 1. Determine the dividend expected at the end of each year during the nonconstant growth period. For example, Apple may be projected to have zero dividends for 2 years, then to establish a $1.00 dividend 2. Estimate the constant growth rate and use it to price the dividend stream that begins after the nonconstant growth period 3. Find the present value of the nonconstant dividends and add the sum to the present value of the price READ AND GO THROUGH EXAMPLES FOR 8.3 & DO PRACTICE QUESTIONS 8.4 The Valuation of Common Stock Using the Stock Repurchases and the Total Payout Model 8.4.1 Stock Repurchases - The repurchase of stock by a firm from its existing stockholders. It is a method to distribute cash without paying dividends Three kinds of repurchase methods 1. Open market o A company instructs its broker to buy shares on the open market at prevailing market prices. The shares are then cancelled and are no longer outstanding. 2. Fixed-price tender offer o 3. Dutch auction o A company announces a target repurchase quantity and invites shareholders to offer their shares for sale. The company provides a range of prices within which it will accept offers. Shareholders select a price in the range and offer a quantity. The company ranks the offers by price and accept the offers up to the point where it achieves its target quantity. All accepted offers receive a price equal to that asked by the last accepted offer. All offers with higher prices are declined. READ AND GO THROUGH EXAMPLES FOR 8.3 & DO PRACTICE QUESTIONS 8.5 Price Earnings Valuation Method P/E ratio is a widely watched measure of how much the market is willing to pay for $1 of earnings from a firm. It is computed as the current market price for a share of stock divided by the earnings per share of the firm. P0 = stock price EPS = proj. earnings per share The avg. P/E can be adjusted up or down to compensate for risk, opportunities, or other factors unique to the firm. The P/E ratio approach is especially useful for valuing privately held firms and firms that do not pay dividends. Ex. Consider Applebee's, the pub restaurant chain. Applebee's earnings-per-share (EPS) is $1.13. The average industry P/E ratio for restaurants is 23. Let's assume that this value is the long-run average P/E for Applebee's. What is the fair price for Applebee's? DO PRACTICE FOR 8.5
