Survey of Investments - Exam 2

Bond value Answered A bond has exactly 4 years until maturity. Its coupon rate is 3%, and the going market yield for a bond of this credit rating and maturity is 5.8%. What is the value of this bond? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a $901.31 b $921.31 c $931.31 d $1,331.31

$901.31

Homework Question 3.2 Stock-X and Stock-Y have expected risk premiums of 10% and 8%, respectively. If the risk-free rate is 3% and you invest 60% in X and 40% in Y, what is the expected return on your portfolio? Enter your answer in percentage points rounded to the nearest two decimal places (i.e., -12.34% should be entered as -12.34). Hint: make sure to keep track of premiums vs. returns.

((10+3)*.6) + ((8 + 3)*.4) = 12.2

Homework Question 3.5 You want to set up a portfolio comprised of three stocks, with the following expected returns:If you invest 30% in Sept, 20% in Oct, and 50% in Nov, what will your expected return be? (Enter the return as in percentage points rounded to the nearest two decimal places; e.g., 10.1234% should be entered as 10.12.) Expected Return Sept Co. 15% Oct Inc. 6% Nov Corp. 22%

(.30*.15 + .2*.6 + .5*.22) = 16.7%

(0,5) (1,12)

(0,5) (1,12) (12 - 5)/(1-0) = 7 equity risk premium

Homework Question 3.4 You currently own a portfolio of one stock, Pink Co., which has an expected return of 12% and a standard deviation of 18%. You want to diversify your holdings by purchasing shares in Blue Inc., which has the following expected return, standard deviation, and correlation with Pink Co. stock:If you buy enough Blue stock to have a portfolio that is 60% Blue and 40% Pink, what will the standard deviation of your new portfolio be? Expected return: 16% Sigma: 24% p = 0.4

(0.4^2 * .18^2 + .6^2 * .24^2 + 2*.6*.4*.18*.24*.4) ^0.5 = 0.005184 0.0207.36 0.0082944 0.0342174 ^0.5 = 0.18497

Homework Question 3.12 Suppose the standard deviation of a stock's firm-specific risk, σ (ei), is 4% and the stock has a beta of 0.9. Meanwhile, the standard deviation of market returns is 20%. What is the standard deviation of the stock's returns (e.g., total risk incorporating both systematic and firm-specific)? Use whole numbers for returns in your calculations, and enter the standard deviation answer in percentage points rounded to the nearest two decimal places. (e.g., if the standard deviation is 15.2425%, enter 15.24.)

(0.9)^2 * (.2)^2 + (.04)^2 = 0.034 Sq(0.034 = 18.44

Forward rates - 2023 yields The yield on 1-year Treasurys is 5.4%. The yield on 2-year Treasurys is 5.1%. Based on the expectations hypothesis, what does this imply next year's yield (the forward rate, f2) will be?

(1 + .051)^2 = (1 + .054) (1 + x) 4.8%

Homework Question 3.9 Your client wants you to invest his wealth partly in risk-free assets and partly in risky assets, to maximize his return given the level of risk he can tolerate. After discussing his risk preferences, savings goals, retirement horizon, etc., he has decided he is comfortable with an annual standard deviation of 10%. You will invest his money accordingly, putting some percent into risk-free t-bills (expected return of 4%) and the rest in your hybrid equity-bond fund, which has an annual standard deviation of 17% and is composed of 40% bonds (expected return of 7%) and 60% equity (expected return of 18%). What percent of your client's money will be invested in the hybrid equity-bond portfolio - that is, what is his capital allocation, y? (Enter the answer in percentage points rounded to the nearest two decimal places; 12.34% should be entered as 12.34.)

(10/17)*100 = 58.8235

Homework Question 3.10 The same client as in the previous problem is comfortable with an annual standard deviation of 10%. You will invest his wealth accordingly, putting some percent into risk-free t-bills (expected return of 4%) and the rest in your hybrid equity-bond fund, which has an annual standard deviation of 17% and is composed of 40% bonds (expected return of 7%) and 60% equity (expected return of 18%). What is the expected return on your client's complete portfolio? (Enter the answer in percentage points rounded to the nearest two decimal places; 12.34% should be entered as 12.34.)

(10/17)*100 = A = 58.8235% B = 1 - 58.8235% = 41.1765% (.4*.07) + (.6*.18) = .136 (.411765*.04) + (.588235*.136) = 9.64272%

Bond Prices at Different Interest Rates

- Longer term bonds have more interest rate risk than short term bonds - Interest rates going down has a greater impact then when bonds go down - if the yield is the same as the coupon that the price should be $1000

Homework Question 3.20 Flash forward 5 years to your successful career as a stock analyst. You've done a thorough valuation of LIFE Inc.'s stock, and believe the stock has an expected return of 16%, given your extensive analysis. Meanwhile the stock has a beta of 0.85. The expected market return and risk-free return are 16.4% and 4.1%, respectively. What is LIFE's alpha? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a 1.45% b 2.06% c -1.45% d -2.06%

.85 (.164-.041) + .041 = .14555 .16 = .14555 + x x = 0.0145

Growth of Invested Funds

0 = -1000 1 = 100 * .1 = 110 2 = 1000 + 100 + (100* .1 = 110) Total = 1210 HPR = (1210 - 1000) / 1000 = .21 Annualize = (1+.21)^1/2 - 1 = .1 or 10%

The Yield Curve - Example 1:

1-yr Zero yielding 8% ; 2-yr Zero yielding 8.5% ÞBond Value 1-yr zero: $925.93 ÞBond Value 2-yr zero: $849.45 What is the implied 1-yr forward rate f2? Þ f2: 1.0852 = 1.08 * (1+f2) Þ f2 = 9.002% Implied value of 2-yr zero 1 year from now? Þ Value of Zero in one year = $1,000/1.09002 = $917.41 The expected one-year HPR on the 2-yr zero? => 917.41 / $849.45 - 1 = 8.00% as it should be - voila!

INTEREST RATE RISK

1. Sell bond at different YTM 2. Reinvestment of coupons

Top hat LLY has a beta of 0.3, while AMZN has a beta of 1.2. If the expected market risk premium is 7%, how much higher should AMZN's expected return be relative to LLY's? (i.e., what is AMZN's expected return minus LLY's expected return)

1.2 - .3 = .9 .9 * 7% = 6.3%

U.S. Treasury Quotes: Treasury note and bond data are representative over-the-counter quotations as of 3pm Eastern time.

1.5% -> 15yr -> $7.50 Ask = 99.05 -> $990.50

Important Implications of the CAPM

1.All investors will choose to hold the market portfolio M and •Weight on each stock = its market cap/aggregate market cap of M •M is on the efficient frontier •M is the optimal portfolio - where CAL is tangent to the efficient frontier 2.All investors will hold a complete portfolio consisting of a proportion invested in M and the remainder in the risk-free asset •Proportions are a function of two factors: the risk premium available on M and the level of individual risk aversion (separation property). 3.Risk premium on M... •Will be proportional to the average level of risk aversion across all investors. •The risk premium on individual assets is proportional to the risk premium on M and the Beta coefficient for the individual asset.

Treasury Bills (T-Bills) - T-Bill discount method flawed for two reasons

1.Yield calculated off face value and not off initial cost (1.96667% versus 2.006% in example) (1.966% => 2.006%) 2.Uses 360-day count rather than 365 (1.966% => 2.006%) BEY is 4.13% rather than 4.0% after adjusting for both flaws

Homework Question 3.6 Two stocks have standard deviations of 16% and 22%, respectively, with a covariance of 172. What is their correlation coefficient? (Note: use whole numbers for returns in your calculations and round your final answer to the nearest two decimal places; e.g., a correlation of 0.22352 should be entered as 0.22.)

172 / (16*22) = .4886

Accrued interest Answered A bond pays coupons semiannually, with a coupon rate of 4%. Its "clean" price is listed as 99.92, but the most recent coupon payment was 40 days ago. Assuming 182 days in a half-year, what is the invoice price (aka "dirty price") of this bond? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a $999.20 b $1,003.60 c $1,020.60

2% * (40/182) = .43956 + 99.92 = 100.35956 = $1,003.60

Top Hat Eden Inc.'s stock has a beta of 0.7. If the risk-free rate is 3% and the expected return on the market is 12%, what should Eden's expected stock return be, according to CAPM?

3 + 0.7(12-3) = 9.3%

Homework Question 3.17 Flash forward 5 years. You're an investment analyst with an intern for the semester who is running analysis on META for you. He turns in a report including an index model estimating META's beta to be 2.1. You check his work and see that the alpha is correct, but he misread the beta, which is actually 1.2. If the expected market return is 10% and the risk-free rate is 4%, how much was the intern overestimating META's expected return? (Enter the return in percentage points rounded to two decimal places; e.g., if the intern's estimate was 14.222% and the correct estimate is 10%, enter 4.22 as your answer). Hint: you won't (and actually can't without alpha) calculate either the correct expected return or the intern's calculation

4 + 2.1(10-4) = 16.6 4 + 1.2(10-4) = 11.2 Overestimate = 5.4

Treasury Bills (T-Bills) example - Bankers discount

4% Price discount 4% * (177/360) from par Price -> 10,000 (1 - .01966667) = 1.96666% -> 9803.33 HRP ( Quoted bond) = (10000 - 9803.33) / 9803.33 = 2.006% BEY (Bond equivalent yield) = 2.006% * (365/177) = 4.137% EAR (Annual effective rate) = (1 + .02006) - 1 = 4.18%

Top Hat You're a financial analyst, studying LaRue Inc. After extensive analysis, you predict a 16% return on LaRue's stock next year. Meanwhile, you estimate its beta to be 1.4. If the expected market return is 12% and the risk-free rate is 5%, what is your estimate of LaRue's alpha?

5 + 1.4(12-5) = 14.8% Prediction: 16% 16% - 14.8% = 1.2%

Top Hat 3 Tbills, pt3 Answered A 6-mo Treasury is quoted with a 5.2% yield. The bill has 145 days until maturity. What is EAR of this security? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a 2.14% b 5.39% c 5.47%

=(1+0.021392)^(365/145) -1 = 0.054727

Top Hat 2

=(10000-9790)/9790.556 =0.021392*(365/145) = 0.05385

Top Hat Tbills, pt1 Unanswered A 6-mo Treasury is quoted with a 5.2% yield. The bill has 145 days until maturity. What is the asking price for this security, assuming the standard par value for T-bills of $10,000? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a 9,793.42 b 9,790.55 c 9,480.00

=5.2*(145/360) = 2.094444 =10000*(1-(2.094444/100)) = 9790.556

Key insight of the CAPM

A security should be priced such that it's E(r) compensates the holder for the additional risk that it contributes to the overall portfolio - given by its β Multiply beta * the market risk premium

Comprehension check

A straight bond is selling at a premium. What must be true about its coupon rate? ◦The bond's coupon rate is higher than the current YTM ◦The bond's coupon rate is lower then the current YTM

The Capital Asset Pricing Model

Assuming everyone is efficient and everyone is diversified. Should be only 1 Optimal risky portfolio Risky vs risk-free

Treasuries (also correctly spelled "Treasurys" sometimes; English is weird) have different labels depending on their maturity: those issued with a maturity less than one year are called Treasury ______________, those issued with a maturity between 1 and 10 years are called Treasury ______________ and those issued with more than 10 years until maturity are called Treasury ______________ Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a Bon

Bills, notes, bonds

Top hat Premiums and discounts 3 straight bonds have a similar characteristics (maturity, credit rating) and thus have the same YTM of 7.3%: Bond A has a coupon rate of exactly 7.3%, Bond B has a coupon rate of 4.5%, and Bond C has a coupon rate of 8.7%. What can you say about the pricing of these bonds?

Bond A (coupon 7.3%) Priced at par Bond B (coupon 4.5%) Priced at a discount Bond C (coupon 8.7%) Priced at a premium

Coupon vs. Required Return

Bond Coupon vs "Market rate of Interest" No matter what the coupon is on a bond, the bond price will adjust such that the bond yield will equal the market rate of interest Bonds of the same (similar): ◦maturity ◦credit quality should be priced to have the same (similar) yield

The Money Market

Bond Equivalent Yield (BEY) ◦Can't compare T-bill bank discount directly to a bond ◦360 vs. 365 days ◦Return is figured in % versus par, not vs. price paid ◦Adjust bank discount rate rBD to make T-Bill comparable to a Treasury or a corporate bond.

Bond Pricing in Excel

Bond Pricing between Coupon Dates ◦Invoice price = Flat price + Accrued interest Bond Pricing in Excel ◦=PRICE (settlement date, maturity date, annual coupon rate, yield to maturity, redemption value as percent of par value, number of coupon payments per year)

Bond Characteristics part 2

Bond Terms Face Value / Par Value / Principal (100) ◦Payment to bondholder at maturity of bond Term: ◦Length of the agreement Coupon Rate ◦Bond's annual interest payment ◦Typically paid semi-annually

The Capital Asset Pricing Model

Capital market and Investor assumptions to achieve efficient market outcome A set of fairly unrealistic assumptions... Later, assumptions will be relaxed to make the model more realistic

The Money Market: Certificates of Deposit (CDs)

Certificates of Deposit Issuer: Depository Institutions Denomination: Any, $100,000 or more marketable (jumbos) Maturity: Varies, Typically 14-day Minimum Liquidity: High for CDs <3 months, if marketable Default Risk: First $250,000 FDIC insured Taxation: Owed: Federal, State, Local

Class 15 - The Money Market

Class 15 - The Money Market

Classes 16 - 17 - Bond prices and yields

Classes 16 - 17 - Bond prices and yields

The Money Market: Commercial PaperThe Money Market: Commercial Paper

Commercial Paper Issuer: Large creditworthy corps.; financial institutions Denomination: Minimum $100,000 Maturity: Maximum 270 days, usually 1-2 months Liquidity: CP < 3 months liquid if marketable Default Risk: Unsecured, rated, mostly high quality Taxation: Owed: Federal, State, Local

Bond Pricing - Convexity

Convexity: An important feature of bond prices ◦ ◦An increase in interest rates (bad) results in a price decline that is smaller than the price gain resulting from a decrease in interest rates (good) of equal magnitude !! We'll talk about this in significant detail in the next slide deck

What percent of the bonds value comes from a coupon vs the par

Coupon - 40/.04*(1 - (1/(1+.04)^60)) Par = 1000/(1+.04)^60

Homework 4.13 The yield to maturity is 6% for 3 different bonds. One is selling at a discount, one at a premium, and one at face value. What can you say about their coupon rates?

Coupon rate is less than 6%: Discount bond Coupon rate is greater than 6%: Face value bond Coupon rate is exactly 6%: Premium bond

Homework Question 3.7 If two stocks can be purchased for a portfolio with weights such that the standard deviation of the portfolio is exactly 0, the correlation between the stocks must be what? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a Exactly 1.0 b Exactly -1.0 c A positive number between 0 and 1 d A negative number between -1 and 0 e Exactly 0

Exactly -1.0 If the standard deviation of a portfolio is exactly 0, it means that there is no variability in the portfolio's returns, indicating a perfect linear relationship between the two stocks. This perfect negative linear relationship is represented by a correlation coefficient of exactly -1.0. A correlation of -1.0 means that the two stocks move in perfect opposite directions. When one stock increases in value, the other decreases by an equal and opposite amount, resulting in a portfolio with no variability in returns, hence a standard deviation of 0.

Self-edification example (try it at home)

Example 10.9 - 40yr, 10% annual coupon, selling at $1,000 => yield of 10% -Holding Period: 20 years -Coupon Re-investment rate: 11% -Market yield for 20-yr bond in 20 years time: 8% What is the HPR? Future Value of all coupons @ 11% = $6,420.28 Value of bond in 20 years at 8% yield = $1,196.36 (value of 20-yr bond) ÞHPR = ($6,420.28+1,196.36) / $1,000 - 1 = 6.6167 (or 661.67%) = (1+6.6167)1/20 -1 = 10.68% per annum

Example: 2 bonds yielding 8%, different coupons

Example: 2 bonds yielding 8%, different coupons Figure 10.6: Coupon 7% (annual, not semi-annual) Market rate: 8% 3 years to maturity: Bond value = $974.23 2 years to maturity: Bond value = $982.17 1 year to maturity: Bond value = $990.74 ($1,000 @ mat.) Coupon 9% (annual, not semi-annual) Market rate: 8% 3 years to maturity: Bond value = $1,025.77 2 years to maturity: Bond value = $1,017.83 1 year to maturity: Bond value = $1,009.26 ($1,000 @ mat.) All bonds approach par value as maturity approaches

Bond HPR: Example

HPR Example A 30 year bond issued with 8% coupon (semi-annual, priced to par) You hold the bond for 6 months, when market interest drops to 7.50%. è Bond Value: $1,059.07 Imagine you sell the bond right after its first coupon date in 6-months: HPR = [($40 + $1,059.07) / $1,000] -1 = 9.91% is the 6-month holding period return. Buy FV = 1000 PMT = 40 I/Y = 4% N = 60 PV = 1000 Sell FV = 1000 PMT = 40 I/Y = 3.75% N = 59 PV = 1059.07 HPR = (40 + 1059.07) / 1000 - 1 9.91%

Treasury Bills (T-Bills) example

Hypothetical Example: T-Bill Yield calculation (bank discount method) ◦Discount quoted: ◦Ask: 4.0% discount (annual) ◦Bid: 4.5% discount ◦Days until maturity: 177 Traditional yield convention for tbills Yield convention foremost bonds

The Capital Asset Pricing Model p2

In Equilibrium ◦Each investor will hold the market portfolio (M) with value weights wi in each stock ◦M is on the efficient frontier, the optimal risky portfolio (point of tangency CAL with eff. frontier) ◦The CML connects the rf rate to M ◦Each security in M is held in proportion (wi) to its market value ◦through buy/sell orders until equilibrium is achieved ◦Investors holding an 'active' portfolio different from M will experience inferior mean-variance outcome ◦Passive investors holding M getting a 'free ride' * Market portfolio is the best

The biggest source of risk in the bond market is... Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a Default risk b Call risk c Liquidity risk d Tax attributes e Interest rate risk

Interest rate risk

Homework 4.25 In normal economic times, yields on short-term Treasuries are ______________ than yields on long-term Treasuries. If this pattern is violated, we say the yield curve is ______________. Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a Lower; convex b Higher; convex c Lower; inverted Your answer d Higher; inverted

Lower; inverted Your answer

Homework Question 3.3 Consider a 3-case scenario analysis for a stock and a bond. What is the covariance for the stock return and bond return? (Note: use decimals for probabilities and whole numbers for returns in your calculations; i.e., multiplying a 30% probability by an 8% return will look like 0.30*8.) Prob(scenario) Stock return Bond Recession 30% -12 8 Slow growth 50% 5 8 Boom 20% 25 -12

Mean Stock Return = (0.30 * -12) + (0.50 * 5) + (0.20 * 25) = -3.6 + 2.5 + 5 = 4.9 Mean Bond Return = (0.30 * 8) + (0.50 * 8) + (0.20 * -12) = 2.4 + 4 + -2.4 = 4 Cov(Stock, Bond) = (0.30 * (-12 - 4.9) * (8 - 4)) + (0.50 * (5 - 4.9) * (8 - 4)) + (0.20 * (25 - 4.9) * (-12 - 4)) Cov(Stock, Bond) = (0.30 * (-16.9) * 4) + (0.50 * 0.1 * 4) + (0.20 * 20.1 * -16) Cov(Stock, Bond) = (-20.13) + (0.2) + (-64.32) Cov(Stock, Bond) = -84.25

The Money Market: Credit Crisis

Money-Market-Mutual-Funds...and the Credit Crisis of 2008 ◦2005-2008: Money market mutual funds (MMMFs) grew 88% ◦MMMFs had their own crisis in 2008: Lehman Brothers ◦Reserve Primary Fund "broke the buck" ◦Run on money market funds ensued ◦U.S. Treasury temporarily offered to insure all money funds (which prevented a total meltdown)

Homework Question 3.1 Which of the following terms refer to risk specific to the firm (not common to the entire economy)? Pick all that apply. Multiple answers: Multiple answers are accepted for this question Select one or more answers and submit. For keyboard navigation...SHOW MORE a Firm-specific risk b Market risk c Systematic risk d Nonsystematic risk e Nondiversifiable risk f Diversifiable risk

Nonsystematic risk Diversifiable risk

Tophat: Bond HPR You buy a bond that has exactly one year left until maturity. Its coupon rate is 6% (paid semi-annually), and when you buy the bond, yields are also 6%. However, before the first coupon payment, yields drop to 5%. You hold the bond until maturity. What is your HPR? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a Exactly 6% b 5.075% c 6.075%

PRB = 1000 Coupon = 6% T = 1 yr 6%/2 = 3% Year 0 = -1000 6 months = 30 1 Year = 1000 + 30 + (30* .025 = .75) 30 + 1000 + 30 + (30* .025 = .75) = 1060.75 (1060.75 - 1000) / 1000 = .06075

A Treasury bill with 170 days left until maturity is quoted with an ask yield of 4%. If the par value is 10,000, what price would you pay for this bond? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a $9,811.11 b $9,871.11 c $9,891.11

Price = Par Value / (1 + (Ask Yield * (Days Left / 360))) Where: Par Value = $10,000 Ask Yield = 4%(0.04 as a decimal) Days Left = 170 Price = $10,000 / (1 + (0.04 * (170 / 360))) Price = $10,000 / (1 + (0.04 * 0.472222)) Price = $10,000 / (1 + 0.01888888) Price = $10,000 / 1.01888888 Price ≈ $9,811.11

Bond Pricing p2

Prices fall as market interest rate rises ◦Interest rate fluctuations are the primary source of bond market risk ◦Bonds with longer maturities are more sensitive to fluctuations in interest rate Other bond risk factors: ◦default risk ◦call risk ◦liquidity risk ◦tax attributes

Bond Yields - Realized Compound Returns vs. YTM

Realized Compound Returns vs. YTM ◦YTM assumes reinvestment of coupons at the YTM Realized compound return ◦Compound rate of return on bond with all coupons reinvested until maturity Reinvestment rate risk ◦Uncertainty surrounding cumulative future value of reinvested coupon payments Horizon analysis Reinvestment of coupons AND the YTM when you sell the bond together determine your total return (HPR) - You assuming that your reinvesting all the coupon payments - You sell the bond at a different interest rate

Bond Yields

Reinvestment rate risk ◦Reinvestment rate risk relevant in a changing interest rate environment Two offsetting effects: ◦Rising interest rates => lower bond value = Price Risk ◦Rising interest rates => higher coupon reinvestment income => re-investment rate risk Price risk is partially offset by reinvestment rate risk as the two move in opposite direction

The Money Market other types

Repurchase Agreements (Repos) ◦Short-term sales of securities with promise to repurchase at higher price ◦Many RPs are overnight; "Term" RPs may have a 1-month maturity - Usually an over night transaction when backs need a certain amount of cash on hand Eurodollars ◦Dollar-denominated time deposits held outside U.S. ◦Pay higher interest rate than U.S. deposits (not regulated, not FDIC insured) Federal Funds ◦Trading in reserves held at the Federal Reserve * ◦Key interest rate for economy LIBOR (London Interbank Offered Rate) ◦Rate at which large banks in London (and elsewhere) lend to each other ◦Base rate for many loans and derivatives ◦Phased out by end of 2021 (replaced by SOFR in U.S.) ◦More on this for Ethics Assignment #1 Bankers' Acceptances ◦Purchaser authorizes a bank to pay a seller for goods at later date (time draft) ◦When purchaser's bank "accepts" draft, it becomes contingent liability of the bank ( and marketable) Reverse Repos ◦Lending money; obtaining security title as collateral ◦"Haircuts" may be required depending on collateral Brokers' Calls ◦Margin Loans ◦Call money rate applies for investors buying stock on margin ◦Loan may be "called in" by broker

SOFR

Secured Overnight Financing Rate - Replaced LIBOR - More trusted

Bond HPR again You buy a bond that has two years left until maturity. Its coupon rate is 6% (paid semi-annually), and when you buy the bond, yields are also 6%. However, before the first coupon payment, yields drop to 5% and remain at 5% until the end of the year, when you sell the bond. What is your HPR? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a Exactly 6% b 5.075% c 6.075% d 7.039%

Selling price Year 0 = -1000 6 months = 30 1 Year = 1000 + 30 + (30* .025 = .75) 2 Year 30 + 1009.6371 + 30 + (30* .025 = .75) = 1070.121 (1070.121 - 1000) / 1000 = .070121

Homework Question 3.8 Chava works at a large investment company, managing one of their mutual funds, one that is restricted to buying only domestic U.S. stocks. She gets transferred to a different fund that can invest in both U.S. and international stocks. Imagine the investment opportunity set (i.e., possible risk-return combinations) Chava faced for her old fund and now for her new fund. Compared to the old fund, the efficient frontier for the new fund is.... Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a Shifted up and to the right b Shifted up and to the left c Shifted down and to the right d Shifted down and to the left e Exactly the same as before

Shifted up and to the left Your answer - Having a broader set of investment opportunities would generally enable a portfolio manager to construct a more efficient portfolio. In other words, it's likely to achieve either: - Higher returns for the same level of risk, or - The same returns but at a lower level of risk. So, when comparing the efficient frontiers, the new efficient frontier with more diverse options would typically be "shifted up and to the left" compared to the old one. Answer: a) Shifted up and to the left

Homework Question 3.15 Consider the two stocks below. Which has a positive beta (i.e., tends to move in the same direction as the market)? Which has a higher R2 (i.e., market returns explain more of its return patterns)? a Stock 1 has a positive beta and a higher R2 b Stock 2 has a positive beta and a higher R2 c Stock 1 has a positive beta, but Stock 2 has a higher R2 Your answer d Stock 2 has a positive beta, but Stock 1 has a higher R2

Stock 1 has a positive beta, but Stock 2 has a higher R2

Terminology for Treasuries:

T-Bills: 1mo - 1 year Discount method T-Notes: 1 - 10 years Semi-Annual T-Bonds: 10 - 30 years Semi-Annual

The Capital Asset Pricing Model p3

The Passive Strategy is Efficient ◦Mutual fund theorem: All investors desire same portfolio of risky assets ◦Implication: 1 mutual fund ◦ ◦Separation Property: 2-step process ◦ ◦If passive strategy is costless and efficient, why follow active strategy? ◦But, what about efficiency? (note: logical inconsistency)

Homework Question 3.13 Which best describes the correlation between systematic and nonsystematic risk (i.e., the market component of the firm's risk and the firm-specific component)? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a The correlation is exactly 1.0 b The correlation is a positive number between 0 and 1 c The correlation is a negative number between -1 and 0 d The correlation is exactly 0

The correlation between systematic and unsystematic risk is exactly 0: Systematic risk Affects all firms and is attributed to broad market factors. Examples include interest, inflation, purchasing power, and market risk. Unsystematic risk Affects only a single firm or industry and can be mitigated through diversification. Examples include poor management, regulatory changes, or litigation. Unsystematic risk is not rewarded because it can be eliminated by investors. Systematic risk is rewarded with a risk premium because it cannot be diversified away.

Homework Question 3.16 Consider the two stocks below. Which has a negative alpha (i.e., tends to underperform the market on a risk-adjusted basis)? Which has more firm-specific risk? (i.e., less of its stock price changes are predicted by market trends)? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a Stock 1 has a negative alpha but Stock 2 has more firm-specific risk b Stock 2 has a negative alpha and more firm-specific risk c Neither has a negative alpha, but Stock 2 has more firm-specific risk d They both have a negative alpha, but Stock 1 has more firm-specific risk

They both have a negative alpha, but Stock 1 has more firm-specific risk

The Money Market

Trading in very short-term debt investments - Cash item on a corporations Balance sheets are commonly invested in money market instruments

The Money Market: Treasury Bills

Treasury Bills Issuer: Federal Government Denomination: Commonly $10,000; min $1,000 Maturity: 4, 13, 26 or 52 Weeks Liquidity: High Default Risk: None Taxation: Owed: Federal; Exempt: State, Local

The biggest sector of the U.S. bond market (by far) is ______________ Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a Corporate bonds b Treasury bonds c Mortgage-backed securities d Bearer bonds

Treasury bonds

The U.S. Financial Market (estimates)

U.S Financial Market U.S. Equity Market Total is c. $52trn U.S. Bond Market Total is c. $52.8trn ◦c. $22.6trn Treasury Bonds ◦c. $12.2trn Mortgage-Backed securities ◦c. $9.9trn Corporate Bonds ◦c. $4.1trn Municipal Bonds ◦c. 4.0trn other - Treasury bill are the biggest part of the bond market - The bond market is roughly the same size as the Equity market

Corporate Bonds

Unlike with Stocks: ◦where the holder receives the full dividend even if stock bought a day before the dividend record date. With Bonds: ◦Bonds are quoted net of Accrued Interest, but ... ◦... Investors have to pay the interest that has accrued to date Bond Invoice = bond price + accrued interest

Bond Characteristics

What is a Bond? ◦IOU ◦Security that obligates issuer to make payments to holder over time ... ◦... and repay the principal at the end

The Money Market: Instrument Yields

When you buy stock, you look at the current price ◦Future value of your investment is not explicitly specified, though you have an expected return in mind When you buy fixed income securities, you look at yield ◦Future value of your investment is specified (par value), so your return (reported in terms of yield) depends on what you pay for it now ◦ These two things are fundamentally equivalent, even though the reporting conventions are different ◦For a stock à Lower price today yields a greater return in the future, for a given expected future value ◦For a bond à Higher yield today means you pay a lower price right now for a determined (though risky) future value

Market Efficiency and Zero Alpha

When α is zero... ◦No reward for bearing firm-specific risk; ◦Extra systematic risk is the only way to earn a higher return Why is α zero? ◦All investors (assumed) to hold diversified portfolios ◦With diversified portfolios à firm-specific risk is diversified away

The Yield Curve

Why should bonds of different maturity offer different yields? 1stAnswer: Expectations Hypothesis ◦Yields to maturity determined solely by expectations of future short-term interest rates Term Structure of Interest Rates: Relationship between yields to maturity and terms to maturity across bonds Strategy 1: 1. buy 1-yr tbill and hold it for a year and then reinvesting in a new 1 year tbill Strategy 2: 1. Buy a 2-yr t-note and hold until maturity Hypothetically they should give you the same holding period return Example for strategy 1: the 1 year treasury is 4% and the expected 1 year return next year is 5%. HPR = (1+.04)*(1+.05) - 1 = 9.2% Example for strategy 2: sq(1+y^2) = 1.092 y2 = 4.498%

Bond Prices Over Time

YTM vs Holding Period Return (HPR) ◦YTM measures average RoR if investment held until maturity ◦HPR is RoR over particular investment period ◦depends on market price at end of period when bond is sold YTM is the expected yield if bond held to maturity; the HPR involves price risk (from changing i rates) HPR involves Price risk and investment rate risk

Bond Yields - Bond HPR before Maturity

Year 0 = 980 Coupons = 75/.06 (1 + .06)^20 - 1) = 27558.92 n = 10 iy = 8 pmt = 75 fv = 1000 = 966.4496 (966.4496 + 27558.92) / 980) - 1 = 2.8014 or 280.14% 2.8014^1/20 = 1.069047934 - 1 = .06904734

Bond Yields

Yield to Maturity (YTM) ◦Discount rate that equates the present value of the bond's payments to its price (bond's IRR). Current Yield ◦Annual coupon divided by bond price Premium/Discount Premium Bonds ◦Bonds selling above par value Discount Bonds ◦Bonds selling below par value - If the coupon is less than the yield than the bond is trading at a discount - If the coupon is more than the yield than the bond is trading at a premium - Yield to maturity is the expected return for this bond - Current yield is different, it is the coupon payments per year/bond price or a one year return

The Money Market: Instrument Yields Problems

Yields on money market instruments not always directly comparable ◦ ◦Factors influencing "quoted" yields ◦Par value vs. investment value ◦360 vs. 365 days assumed in a year (366 leap year) ◦Simple vs. compound interest Think of yield as a "return" that is reported according to some convention... •...and that we may need to adjust in order to understand the true expected return Problems with bond yields* 1. Based on FV no PV Example: Return stock = (PS - PB) / PB discount yield = (PS - PB) / PS 2. 360 day-year 3. Ignore compounding

Special Case Zero coupon bond

Zero-Coupon Bond ◦Pays no coupons, ◦sells at discount to par value, ◦provides only one payment: par value at maturity

Because t-bill yields are quoted with the discount method, their quoted yields are not directly comparable to bond-equivalent yields (i.e., how typical longer-maturity bonds are quoted) for what reasons? Choose the two that apply: Multiple answers:Multiple answers are accepted for this question Select one or more answers and submit. For keyboard navigation...SHOW MORE a The bank discount yield is calculated off of face value¸ rather than initial buy price b The bank discount yield assumes conti

a The bank discount yield is calculated off of face value¸ rather than initial buy price c The bank discount yield assumes a 360 (rather than the true 365 or 366) day year

Homework Question 3.19 According to CAPM, which of the following are true under an efficient market? Pick all that apply. a Alpha is always 0 for all stocks Your answer b Alpha is positive only for very risky stocks c Only professional money managers can achieve a Sharpe ratio higher than the market's d No one can achieve a Sharpe ratio higher than the market's e Everyone will optimally invest in the market portfolio for the risky portion of their complete portfolio Your answer f The only way to earn higher returns than the market is to invest in stocks with high firm-specific risk g The only way to earn higher returns than the market is to increase the beta of your portfolio

a) Alpha is always 0 for all stocks. (True) e) Everyone will optimally invest in the market portfolio for the risky portion of their complete portfolio. (True) g) The only way to earn higher returns than the market is to increase the beta of your portfolio. (True)

Homework Question 3.18 Which of the following line types that we've discussed plots returns in the y-axis and a risk metric in the x-axis? Pick all that apply. a CAL b CML Your answer c SCL d SML

a) CAL (Capital Allocation Line) b) CML (Capital Market Line) d) SML (Security Market Line)

Homework 4.24 An analyst wants to estimate the 1-year forward rate, f2. She checks the yields on 2 zero coupon bonds with similar risk profiles, one with 2 years until maturity and a yield of 8%, the other with 1 year until maturity and a yield of 7%. She settles on an estimate of 8.61% for the forward rate. Assume her math is right. How do you think she determined this rate? a The expectations hypothesis directly implies a forward rate of 8.61% b She incorporated a liquidity premium in her ca

b She incorporated a liquidity premium in her calculations, which makes her forward rate lower than the pure prediction from the expectations hypothesis. The forward rate she determined (8.61%) is higher than the 1-year yield (7%) but lower than the yield on the 2-year bond (8%). This suggests that she incorporated a liquidity premium into her estimate, which typically results in a forward rate higher than the pure prediction from the expectations hypothesis.

Homework Question 3.21 Consider the following two stocks, with your estimated expected returns, based on fundamental analysis, along with the returns predicted from CAPM. Pick the two statements from the following that are true if your analysis is correct: Expected return CAPM prediction Georgia Co. 15% 16% Dawgs Inc. 17% 16% A Dawgs is overpriced b Georgia is overpriced c Dawgs is underpriced d Georgia is underpriced

b) Georgia is overpriced. c) Dawgs is underpriced. Georgia Co.'s expected return (15%) is lower than its CAPM prediction (16%). Dawgs Inc.'s expected return (17%) is higher than its CAPM prediction (16%).

Homework Question 3.11 You want to estimate the monthly alpha and beta of AXON stock, using the index model. Suppose AXON has a beta of 0.95 and a monthly alpha of 0.5 (representing half a percent). If you set up the regression model correctly, the index model equation should be (remember in index model formulas, we use R instead of r to denote excess returns): Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer.

d) R_{axon} = 0.95 * R_{market} + 0.5 In the index model, the excess return of a stock (R_{axon}) is regressed against the excess return of the market (R_{market), and the coefficient of the market's return represents the beta (0.95 in this case), while the intercept represents the alpha (0.5).

Homework Question 3.25

d) e (error term) The difference between the predicted return and the actual return in a regression analysis is typically due to the error term (residual error). Therefore, the correct answer is:

accured interest

interest accumulated at a given time but not yet due or paid Coupon rate = 5% semiannual Last coupon 45 days ago = Coupon * 45/182 = 2.5 * .2473 =6.18 Dirty price = 1011.20 + 6.18 = 1017.38

The α of the Regression

α = 0.8751% Over the 60 months Google stock was above the SML. However, ◦The Standard Error of α estimate = 1.09 ◦t-statistic = 0.8751 / 1.09 = 0.801 is very low signaling statistical insignificance of the estimate ◦p-value = the probability that pure chance could have produced the same estimate for α ◦Here, p-value = 42.6% The estimate for α is NOT statistically significant

The Yield Curve - Forward Rates

◦A set of future interested rates, imputed from today's yield curve, that makes: ◦ E(r) of long-term bond equal to that of rolling over short-term bonds ◦The array of implied forward rates, technically, is called the term-structure of interest rates ◦Best imputed from zeros but coupon bonds will do

The Yield Curve

◦Graph of yield to maturity as function of term to maturity

The Yield Curve - Example cont'd

◦In the 2yr example on the previous page, an investor would be indifferent between investing in the 1yr rate today and rolling that over into the second year ... ◦or ◦... to buy the 2yr bond today

The Yield Curve - 2nd Answer: Liquidity Preference Theory

◦Investors demand a risk premium on long-term bonds ◦SD of returns increases with term of bond ◦Liquidity (secondary market) decreases with term of bond Liquidity premium ◦Extra return demanded by investors as compensation for greater risk of long-term bonds ◦Spread between expected and imputed forward rates

The Security Market Line (SML)

◦Represents expected return-beta relationship of CAPM ◦Graphs security risk premium as a function of β (security risk) ◦β is proportional to the systematic variance the stock adds to a portfolio Alpha: ◦Abnormal rate of return on a security in excess of that predicted by the CAPM Beating the market compared to the CAPM expected return based on what a stocks risk justifies + Alpha implies that a stock is over priced - Alpha implies that a stock is underpriced

The CML vs SML

◦The CML graphs risk premia of complete portfolio as a function of the market portfolio ◦Special case of the CAL ◦The SML graphs individual security risk premium as a function of β (i.e. how much systematic risk the security adds) ◦The SCL in ch. 6 graphs the return for a particular stock; the SML is the benchmark for every traded security

The Money Market: Instruments

◦Treasury Bills (T-Bills) ◦Certificates of Deposit (CDs) ◦Commercial Paper (CP) ◦Bankers' Acceptances ◦Eurodollars ◦Repos and Reverses ◦Brokers' Funds ◦Federal Funds ◦LIBOR (London Interbank Offer Rate) phased out after 2021 - Treasuries or Treasurys

Applications of CAPM

◦Use SML as benchmark for fair return on risky asset ◦SML provides "hurdle rate" for equity-financed projects ◦Capital budgeting ◦α exists only for mispriced assets ◦Incentive for active managers