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Ch 1:Investments & Financial Assets

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1 Ch 1:Investments & Financial Assets
Essential nature of investment Reduced current consumption Planned later consumption Consumption Timing Allocation of Risk Two main themes of investments Modern Portfolio theory (MPT): Risk-return trade off in the securities markets Efficient diversification Capital asset pricing and valuation Efficient Market Hypothesis (EMH): security price reflects all the information available to investors concerning the value of the securities Real Assets Assets used to produce goods and services Financial Assets Claims on real assets Ch1: Page 1-6 Ch2: Page 7-27 Ch3: Page 28-52 Ch5:Page 53-86

2 Major Classes of Financial Assets or Securities
Debt Money market instruments Bonds Equity Common stock Preferred stock Derivative securities

3 Agency Issues and Crisis in Corporate Governance
Accounting Scandals Examples – Enron and WorldCom Analyst Scandals Example – Citigroup’s Salomon Smith Barney Initial Public Offerings Credit Swiss First Boston

4 The Agency Problem Agency relationship
Principal hires an agent to represent their interest Stockholders (principals) hire managers (agents) to run the company Two conditions of agency problem: 1. Conflict of interest between principal and agent 2. Asymmetric information Management goals and agency costs Video Note: This video focuses on how one company handled the tough decision to cut jobs and managed to successfully increase shareholder value. It features ABT Co. in Canada. A common example of an agency relationship is a real estate broker – in particular if you break it down between a buyers agent and a sellers agent. A classic conflict of interest is when the agent is paid on commission, so they may be less willing to let the buyer know that a lower price might be accepted or they may elect to only show the buyer homes that are listed at the high end of the buyers price range. Ethics Note: The instructor’s manual provides a discussion of Gillette and the apparent agency problems that existed prior to the introduction of the sensor razor. Direct agency costs – the purchase of something for management that can’t be justified from a risk-return standpoint, monitoring costs. Indirect agency costs – management’s tendency to forgo risky or expensive projects that could be justified from a risk-return standpoint.

5 The Investment Process
A Top-Down Analysis of Portfolio Construction the Capital Allocation decision Choice of safe but low-return money market securities, or risky but higher-return securities (e.g., stocks) the Asset Allocation decision the distribution of risky investments across broad asset classes like stocks, bonds, real estates, foreign assets, and so on. the Security Selection decision the choice of which particular securities to hold within each asset class security analysis involves the valuation of particular securities: must forecast dividends and earnings fundamental/ technical analysis Market efficiency

6 Active vs. Passive Management
Active Management Finding undervalued securities Timing the market Passive Management No attempt to find undervalued securities No attempt to time Holding an efficient portfolio

7 Major Financial Markets and Assets or Securities
Money market Treasury bills, Certificates of deposits, Commercial Paper, Bankers Acceptances, Eurodollars, Repurchase Agreements (RPs) and Reverse RPs, Brokers’ Calls, Federal Funds, etc. Treasury bills most marketable; highly liquid; discount bond maturities: 28, 91, 182 days minimum denomination: $1,000 Issued weekly

8 Costs of Trading Commission: fee paid to broker for making the transaction Spread: cost of trading with dealer Bid: price dealer will buy from you Ask: price dealer will sell to you Spread: ask - bid Combination: on some trades both are paid

9 Ch 2:Asset classes and financial instruments Figure 2.2 Treasury Bills

10 T-bill T.B yields are quoted as the “bank discount yield”
rBD = 10,000 - P x 360 10, n where P = the bond price; n = the maturity in days; rBD = the bank discount yield; $10,000 = par value. To determine the T-bill’s true market price: P = 10,000 x [ 1 - rBD x n/360 ] Ex. T-bill sold at $9,500 with a maturity of a half year (182 days): rBD= (500/10,000) x (360/182) = (9.89%) The “bond equivalent yield” of the T-bill = APR (annual percentage rate) rBEY = (10,000 - P)/P x (365/n) = (500/9,500) x (365/182) = % Effective annual yield: reay ( /9,500 ) = (10.8%) note: rBD < rBEY < rEAY What is the asked price, equivalent yield, and effective yield for the T-Bill marked red in previous slide? RBEY = 365*rBD/(360-n*rBD)

11 Major Financial Markets and Assets or Securities
Bond market Treasury Notes and Bonds Maturities Notes – maturities up to 10 years Bonds – maturities in excess of 10 years 2001 Treasury suspended sales Note: 11/1/2001: The Treasury department would no longer sell 30-year bonds, for years the benchmark for the entire $17.7 trillion U.S. bond market – long-term interest rate will decline. Now 10-year Treasury takes over the benchmark title resume sales Par Value - $1,000 Quotes – percentage of par

12 Figure 2.4 Treasury Notes, Bonds and Bills

13 Example12 1. If a treasury note has a bid price of $982.50, the quoted bid price in the Wall Street Journal would be __________. A) $98:08 B) $98:25 C) $98:50 D) $98:40 2. The price quotations of treasury bonds in the Wall Street Journal show an ask price of 104:16 and a bid price of 104:08. As a buyer of the bond you expect to pay __________. A) $1,041.60 B) $1,045.00 C) $1,040.80 D) $1,042.50 A Given $982.5, we have 982.5/1000% = 98.25, = x/32, x = 8, therefore the quoted bid price is 98:08.  2. B Step 1: Buyer are able to take asked price, 104:16. Step 2: 16/32 = 0.5, then 104:16 becomes 104.5 Step3: 104.5*1000% = $1045

14 Example 34 3. Suppose you pay $9,800 for a Treasury bill maturing in two months. What is the annual percentage rate of return for this investment? A) 2% B) 12% C) 12.2% D) 16.4% 4. Suppose you pay $9,700 for a Treasury bill maturing in six months. What is the effective annual rate of return for this investment? A) 3.1% B) 6% C) 6.18% D) 6.28% 3. C APR = [( )/9800]*12/2 =12.2% 4. D EAR = (1+APR/m)^m -1=(1+( )/9700)^(12/6) =6.28%

15 Municipal Bonds Issued by state and local governments
Interest income is exempt Types General obligation bonds Revenue bonds Industrial revenue bonds Maturities – range up to 30 years

16 Municipal Bond Yields Interest income on municipal bonds is not subject to federal and sometimes state and local tax r = rm / (1 - t), where rm = the rate on municipal bonds; t = the investor’s marginal tax bracket; r = the total before-tax rate of return on taxable bonds. Ex. rm = 10%; t = 28% : then r = %, if t = 36%: then r = % Ex. A municipal bond carries a coupon of 6% and is trading at par; to a taxpayer in a 36% tax bracket, What is the taxable equivalent yield of this bond ?

17 Corporate Bonds Issued by private firms Semi-annual interest payments
Subject to larger default risk than government securities Options in corporate bonds Callable Convertible

18 Figure 2.8 Corporate Bond Prices

19 Example31 1. The purchase price for a bond is listed as 104 and the annual coupon rate is 4.3%. What is the current yield (annual coupon payment / current price) on this bond? A) 0.00% B) 4.00% C) 4.13% D) 4.30% 2. What is the tax exempt equivalent yield on a 9% bond yield given a marginal tax rate of 28%? A) 6.48% B) 7.25% C) 8.02% D) 9.00% C Quote of 104 means $1040, annual coupon payment = 4.3% *1000 = 430; current yield = 430/1040 = 4.13% 2. A 9%*(1-0.28) = 6.48%

20 Equity Markets Common stock Preferred stock Depository receipts
Residual claim Limited liability Preferred stock Fixed dividends - limited Priority over common Tax treatment Depository receipts

21 Figure 2.10 Listing of Stocks Traded on the NYSE

22 Uses of Stock Indexes Track average returns
Comparing performance of managers Base of derivatives

23 Factors for Construction of Stock Indexes
Representative? Broad or narrow? How is it weighted?

24 Examples of Indexes - Domestic
Dow Jones Industrial Average (30 Stocks) Standard & Poor’s 500 Composite NASDAQ Composite NYSE Composite Wilshire 5000 CurrentlyDJIA: Alcoa, Allied Signal, American Express, American International Group Inc, Boeing, Caterpillar, Citigroup, Coca-Cola, DuPont, Exxon, General Electric, General Motors, Hewlett-Packard, Home Depot, IBM, Intel, Johnson & Johnson, McDonald, Merck, Microsoft, 3M, JP Morgan, Pfizer, Phillip Morris, Proctor& Gamble, SBC Communications, United Technologies, Verizon Communications, Wal-Mart Stores, Walt Disney.

25 Construction of Indexes
How are stocks weighted? Price weighted (DJIA) (p40 example 2.2) Market-value weighted (S&P500, NASDAQ) (p46 example 2.4) S&P 500 Index = [Pit Qit / O.V. ] x 10 where O.V. = original valuation in (i.e., relative to the average value during the period of , which was assigned an index value of 10) 81% of the mkt value of companies on the NYSE Equally weighted (Value Line Index) Stock IP FP shares IV FV ABC 25 30 20 500 600 XYZ 100 90 1 Total 690

26 Derivatives Securities
Options Basic Positions Call (Buy) Put (Sell) Terms Exercise Price Expiration Date Assets Futures Basic Positions Long (Buy) Short (Sell) Terms Delivery Date Assets

27 Example33 1. The Chompers Index is a price weighted stock index based on the 3 largest fast food chains. The stock prices for the three stocks are $54, $23, and $44. What is the price weighted index value of the Chompers Index. A) 23.43 B) 35.36 C) 40.33 D) 49.58 2. A benchmark index has three stocks priced at $23, $43, and $56. The number of outstanding shares for each is 350,000 shares, 405,000 shares, and 553,000 shares, respectively. If the market value weighted index was 970 yesterday and the prices changed to $23, $41, and $58, what is the new index value? A) 960 B) 970 C) 975 D) 985 C ( )/3 = 40.33 Yesterday market value = 23* * * = , Today’s market value = 23* * * = New index value = 970* / = 975

28 Ch3: Security markets Primary vs. Secondary Security Sales
New issue Key factor: issuer receives the proceeds from the sale Secondary Existing owner sells to another party Issuing firm doesn’t receive proceeds and is not directly involved

29 How Firms Issue Securities
Investment Banking Shelf Registration Private Placements Initial Public Offerings (IPOs)

30 Investment Banking Arrangements
Underwritten vs. “Best Efforts” Underwritten: firm commitment on proceeds to the issuing firm Best Efforts: no firm commitment Negotiated vs. Competitive Bid Negotiated: issuing firm negotiates terms with investment banker Competitive bid: issuer structures the offering and secures bids

31 Figure 3.1 Relationship Among a Firm Issuing Securities, the Underwriters and the Public

32 Initial Public Offerings
Process Road shows: 1. generate interest among potential investors and provide information about the offering. 2. provide price information to the issuing firm and its underwriters. Bookbuilding: process of polling potential investors Underpricing Post sale returns Cost to the issuing firm

33 Figure 3.4 Long-term Relative Performance of Initial Public Offerings

34 Stock Market Order Types
Buy at best price available for immediate execution. Sell at best price available for immediate execution. Buy Sell Limit order Buy at best price available, but not more than the preset limit price. Forgo purchase if limit is not met. Sell at best price available, but not less than the preset limit price. Forgo sale if limit is not met. Stop orders convert to a market order to buy when the stock price crosses the stop price from below. convert to a market order to sell when the stock price crosses the stop price from above

35 Limited Order and Stop order
Ex. Stock A selling $25: a limit $23 [instruct the broker to buy when price falls below $23]; a limit [to sell when price goes above $27] Stop-loss (sell) orders [ex. Stop to sell if price falls a stipulated level to sell to stop further losses from accumulating Stop-buy orders [ex. Stop buy to buy when price rises above a given limit accompany short sales, to limit potential losses from the short position (problem 20, 21)

36 Order Specification and Trading Mechanisms
name of Company buy or sell size of order (odd lots = less than 100 shares; round lots = 100 shares) how long is order to be outstanding (when expires) types of order Dealer markets Electronic communication networks (ECNs) Specialists markets

37 U.S. Security Markets Nasdaq Small stock OTC Organized Exchanges
Pink sheets Organized Exchanges New York Stock Exchange American Stock Exchange Regionals Electronic Communication Networks (ECNs) National Market System

38 OTC (Nasdaq) No central physical location
No membership requirements for trading: brokers register with the SEC as dealers in OTC dealer market: quote bid & asked prices and execute, over 400 market makers note: bid (asked) price: at which a dealer is willing to purchase (sell) about 35,000 issues are traded NASD (National Association of Sec. Dealers) oversees trading of OTC securities in 1971, the NASDAQ system began The Nasdaq composite Index includes about 3,400 companies (about 5,000 companies in 2000) whose weight in the index is based on market capitalization Nasdaq operates two market segments: Nasdaq National Market and Nasdaq SmallCap Market (listing requirements differ)

39 New York Stock Exchange
A facility (central physical location) Only members may trade The NYSE membership is limited to 1,366 members since 1953, who collectively own the NYSE. The NYSE represents approximately 80% of the value of all publicly owned companies in America. Memberships (or seats) are valuable assets ($1 mil:1/6/2005, $1.7 mil: 4/3/00, $2 mil in 2003) Member functions Commission brokers Floor brokers Specialists

40 Margin Trading Using only a portion of the proceeds for an investment
Borrow remaining component Margin arrangements differ for stocks and futures Margin is the net worth of the investor’s account

41 Stock Margin Trading Maximum margin is currently 50%; you can borrow up to 50% of the stock value Set by the Fed Maintenance margin: minimum amount equity in trading can be before additional funds must be put into the account Margin call: notification from broker you must put up additional funds

42 Margin Trading - Initial Conditions
X Corp $70 50% Initial Margin 40% Maintenance Margin Shares Purchased Initial Position Stock $70,000 Borrowed $35,000 Equity ,000

43 Margin Trading - Maintenance Margin
Stock price falls to $60 per share New Position Stock $60,000 Borrowed $35,000 Equity ,000 Margin% = Equity/Asset =$25,000/$60,000 = 41.67%

44 Margin Trading - Margin Call
How far can the stock price fall before a margin call? (1000P - $35,000)* / 1000P = 40% P = $58.33 * 1000P - Amt Borrowed = Equity

45 Short Sales Purpose: to profit from a decline in the price of a stock or security Mechanics Borrow stock through a dealer Sell it and deposit proceeds and margin in an account. allowed only after an ‘uptick’ (P > 0) Closing out the position: buy the stock and return to the party from which is was borrowed

46 Liabilities & Account Equity
Short Sales Example: Short Sales You want to short 100 Sears shares at $30 per share. Your broker has a 50% initial margin and a 40% maintenance margin on short sales. Worth of stock borrowed = $30 × 100 = $3,000 Liabilities & Account Equity Assets Proceeds from sale $3,000 Short position $ 3,000 Initial margin deposit 1,500 Account equity 1,500 Total $4, Total $4,500

47 Liabilities & Account Equity
Short Sales Example: Short Sales …continued Scenario 1: The stock price falls to $20 per share. Liabilities & Account Equity Assets Proceeds from sale $3,000 Short position $ 2,000 Initial margin deposit 1,500 Account equity 2,500 Total $4, Total $4,500 New margin = equity/short position = $2,500 / $2,000 = 125%

48 Liabilities & Account Equity
Short Sales Example: Short Sales …continued Scenario 2: The stock price rises to $40 per share. Liabilities & Account Equity Assets Proceeds from sale $3,000 Short position $ 4,000 Initial margin deposit 1,500 Account equity (A-L) 500 Total $4, Total $4,500 New margin = equity/short position=$500 / $4,000 = 12.5% < 40% Therefore, you are subject to a margin call.

49 Short Sale - Initial Conditions
Z Corp 100 Shares 50% Initial Margin 30% Maintenance Margin $100 Initial Price Sale Proceeds $10,000 Margin & Equity 5,000 Stock Owed 10,000

50 Short Sale - Maintenance Margin
Stock Price Rises to $110 Sale Proceeds $10,000 Initial Margin ,000 Stock Owed ,000 Net Equity ,000 Margin % (4000/11000) %

51 Short Sale - Margin Call
How much can the stock price rise before a margin call? ($15,000* - 100P) / (100P) = 30% P = $115.38 * Initial margin plus sale proceeds

52 Example 23 1. Assume you purchased 200 shares of XYZ common stock on margin at $80 per share from your broker. If the initial margin is 60%, the amount you borrowed from the broker is __________. A) $4000 B) $6400 C) $9600 D) $16,000 2. You short-sell 200 shares of Tuckerton Trading Co., now selling for $50 per share. What is your maximum possible gain ignoring transactions cost? A) $50 B) $150 C) $10,000 D) unlimited B 200*80*40% = 6400 2. C Maximum gain = 200*50 = 10,000

53 Ch 5: Risk and return: Past and prologue Holding Period Return

54 Rates of Return: Single Period Example
Ending Price = 24 Beginning Price = 20 Dividend = 1 HPR = ( )/ ( 20) = 25%

55 Example 43 You purchased a share of stock for $20. One year later you received $2 as dividend and sold the share for $23. Your holding-period return was __________. A) 5 percent B) 10 percent C) 20 percent D) 25 percent The holding period return on a stock was 25%. Its ending price was $18 and its beginning price was $16. Its cash dividend must have been __________. A) $0.25 B) $1.00 C) $2.00 D) $4.00 D HPR = ( )/20 = 25% 2. C 0.25 = (18-16+D)/16, D = 2

56 Returns Using Arithmetic and Geometric Averaging
ra = (r1 + r2 + r rn) / n ra =.10 or 10% Geometric rg = {[(1+r1) (1+r2) .... (1+rn)]} 1/n - 1 rg = = 8.29%

57 Example 12 1. The arithmetic average of 12%, 15% and 20% is _________.
B) 15% C) 17.2% D) 20% 2. The geometric average of 10%, 20% and 25% is __________. A) 15% B) 18.2% C) 18.3% D) 23% A ( )/3 = 15.7% 2. B [(1+0.1)*(1+0.2)*(1+0.25)]^(1/3) – 1 = 18.2%

58 Quoting Conventions APR = annual percentage rate
(periods in year) X (rate for period) EAR = effective annual rate ( 1+ rate for period)Periods per yr - 1 Example: monthly return of 1% APR = EAR =

59 Characteristics of Probability Distributions
1) Mean: most likely value 2) Variance or standard deviation 3) Skewness * If a distribution is approximately normal, the distribution is described by characteristics 1 and 2

60 Return Variability: The Second Lesson
1 - 60 Return Variability: The Second Lesson

61 Example What range of return would you expect to see in 95% of time?
Is it possible you can earn 65% return annually at 1% significant level? -26.9% to 53.5%; Yes.

62 Measuring Mean: Scenario or Subjective Returns
Subjective expected returns E ( r ) = p s S p(s) = probability of a state r(s) = return if a state occurs 1 to s states

63 Numerical Example: Subjective or Scenario Distributions
State Prob. of State rin State E(r) =.15

64 Measuring Variance or Dispersion of Returns
Subjective or Scenario Variance = S s p ( ) [ r - E )] 2 Standard deviation = [variance]1/2 Using Our Example: Var=.01199 S.D.= [ ] 1/2 = .1095

65 Historical mean and standard deviation

66 Risk Premiums and Risk Aversion
Degree to which investors are willing to commit funds Risk aversion If T-Bill denotes the risk-free rate, rf, and variance, , denotes volatility of returns then: The risk premium of a portfolio is: E(Rp) - Rf

67 Risk Premiums and Risk Aversion
To quantify the degree of risk aversion with parameter A: E(Rp) – Rf = (1/2) A σp2

68 The Sharpe (Reward-to-Volatility) Measure
Sharpe ratio = Portfolio risk premium/standard deviation of the excess returns = (E(Rp) – Rf )/σp

69 Annual Holding Period Returns From Table 5.3 of Text
Geom. Arith. Stan. Series Mean% Mean% Dev.% World Stk US Lg Stk US Sm Stk Wor Bonds LT Treas T-Bills Inflation

70 Figure 5.1 Frequency Distributions of Holding Period Returns

71 Figure 5.2 Rates of Return on Stocks, Bonds and Bills

72 Real vs. Nominal Rates Fisher effect: Approximation
nominal rate = real rate + inflation premium R = r + i or r = R - i Example r = 3%, i = 6% R = 9% = 3% + 6% or 3% = 9% - 6% Fisher effect: Exact r = (1+R) / (1 + i) - 1 2.83% = (9%-6%) / (1.06)

73 Figure 5.4 Interest, Inflation and Real Rates of Return

74 Allocating Capital Between Risky & Risk-Free Assets
Possible to split investment funds between safe and risky assets Risk free asset: proxy; T-bills Risky asset: stock (or a portfolio) Risk premium: risk asset return-risk-free rate Issues Examine risk/ return tradeoff Demonstrate how different degrees of risk aversion will affect allocations between risky and risk free assets

75 Example: Given: rf = 7% srf = 0% E(rp) = 15% sp = 22% y = % in p
(1-y) = % in rf

76 Expected Returns for Combinations
E(rc) = yE(rp) + (1 - y)rf rc = complete or combined portfolio For example, y = .75 E(rc) = .75(.15) + .25(.07) = .13 or 13%

77 Variance on the Possible Combined Portfolios
= 0, then s p c = Since rf y s s

78 Combinations Without Leverage
= .75(.22) = .165 or 16.5% If y = .75, then = 1(.22) = .22 or 22% If y = 1 = 0(.22) = .00 or 0% If y = 0 s s s

79 Using Leverage with Capital Allocation Line
Borrow at the Risk-Free Rate and invest in stock Using 50% Leverage rc = (-.5) (.07) + (1.5) (.15) = .19 sc = (1.5) (.22) = .33 Reward-to-variability ratio = risk premium/standard deviation

80 Figure 5.5 Investment Opportunity Set with a Risk-Free Investment

81 Figure 5.6 Investment Opportunity Set with Differential Borrowing and Lending Rates

82 Risk Aversion and Allocation
Greater levels of risk aversion lead to larger proportions of the risk free rate Lower levels of risk aversion lead to larger proportions of the portfolio of risky assets Willingness to accept high levels of risk for high levels of returns would result in leveraged combinations

83 Example 22 1. Consider the following two investment alternatives. First, a risky portfolio that pays 15% rate of return with a probability of 60% or 5% with a probability of 40%. Second, a treasury bill that pays 6%. The risk premium on the risky investment is __________. A) 1% B) 5% C) 9% D) 11% 2. Consider the following two investment alternatives. First, a risky portfolio that pays 20% rate of return with a probability of 60% or 5% with a probability of 40%. Second, a treasury that pays 6%. If you invest $50,000 in the risky portfolio, your expected profit would be __________. A) $3,000 B) $7,000 C) $7,500 D) $10,000 1.B Risk premium = Rp- Rf = (0.60)*(0.15)+(0.40)*(0.05) – 0.06 = 11%-6% = 5% 2.B Rp = (0.60)(0.20)+(0.40)(0.05) = 14%; profit = 0.14*50000 = 7,000

84 Example 41 3.You have $500,000 available to invest. The risk-free rate as well as your borrowing rate is 8%. The return on the risky portfolio is 16%. If you wish to earn a 22% return, you should __________. A) invest $125,000 in the risk-free asset B) invest $375,000 in the risk-free asset C) borrow $125,000 D) borrow $375,000 4.The Manhawkin Fund has an expected return of 12% and a standard deviation return of 16%. The risk free rate is 4%. What is the reward-to-volatility ratio for the Manhawkin Fund? A) 0.5 B) 1.3 C) 3.0 D) 1.0 3. D 0.22= y*0.16+(1-y)*0.08, y = 1.75, 1-y = -0.75, (1-y)* = -0.75* = -375,000, negative means borrowing. 4. A S = (Rp-Rf)/σ = ( )/.16 = 0.5

85 Example 422 5.You invest $100 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 12% and a standard deviation of 15% and a treasury bill with a rate of return of 5%. __________ of your money should be invested in the risky asset to form a portfolio with an expected rate of return of 9% A) 87% B) 77% C) 67% D) 57% 6.An investor invests 40% of his wealth in a risky asset with an expected rate of return of 15% and a variance of 4% and 60% in a treasury bill that pays 6%. Her portfolio's expected rate of return and standard deviation are __________ and __________ respectively. A) 8.0%, 12% B) 9.6%, 8% C) 9.6%, 10% D) 11.4%, 12% 7.The expected return of portfolio is 8.9% and the risk free rate is 3.5%. If the portfolio standard deviation is 12.0%, what is the reward to variability ratio of the portfolio? A) 0.0 B) 0.45 C) 0.74 D) 1.35 5.D 0.09 = y*(0.12)+(1-y)*0.05, y = 57% 6.B Rc = (0.4)*(0.15)+(0.60)*(0.06) = 9.6%, σc = yσp =(0.4)sqrt(0.04) = 8% 7.B S = ( )/12 = 0.45

86 Efficient Diversification
Ch 6 Efficient Diversification

87 Diversification and Portfolio Risk
Total risk: Market risk Systematic or Nondiversifiable Firm-specific risk Diversifiable or nonsystematic or unique

88 Figure 6.1 Portfolio Risk as a Function of the Number of Stocks

89 Figure 6.2 Portfolio Risk as a Function of Number of Securities

90 Exercise 42 1. Risk that can be eliminated through diversification is called ______ risk. A) unique B) firm-specific C) diversifiable D) all of the above 2. The risk that can be diversified away is ___________. A) beta B) firm specific risk C) market risk D) systematic risk D B

91 Two Asset Portfolio Return – Stock and Bond

92 Covariance Cov(r1r2) = r1,2s1s2 r1,2 = Correlation coefficient of
returns s1 = Standard deviation of returns for Security 1 s2 = Standard deviation of returns for Security 2

93 Correlation Coefficients: Possible Values
Range of values for r 1,2 -1.0 < r < 1.0 If r = 1.0, the securities would be perfectly positively correlated If r = - 1.0, the securities would be perfectly negatively correlated

94 Two Asset Portfolio St Dev – Stock and Bond

95 In General, For an n-Security Portfolio:
rp = Weighted average of the n securities sp2 = (Consider all pair-wise covariance measures)

96 Numerical Example: Bond and Stock
Returns Bond = 6% Stock = 10% Standard Deviation Bond = 12% Stock = 25% Weights Bond = .5 Stock = .5 Correlation Coefficient (Bonds and Stock) = 0

97 Return and Risk for Example
.5(6) + .5 (10) Standard Deviation = 13.87% [(.5)2 (12)2 + (.5)2 (25)2 + … 2 (.5) (.5) (12) (25) (0)] ½ [192.25] ½ = 13.87

98 Figure 6.3 Investment Opportunity Set for Stock and Bonds

99 Minimum variance portfolio
Ws = [σB2 - Cov(rS, rB)] / (σs2 + σB2 -2Cov(rS, rB))

100 Figure 6.4 Investment Opportunity Set for Stock and Bonds with Various Correlations

101 Extending to Include Riskless Asset
The optimal combination becomes linear A single combination of risky and riskless assets will dominate

102 Figure 6.5 Opportunity Set Using Stock and Bonds and Two Capital Allocation Lines

103 Dominant CAL with a Risk-Free Investment (F)
CAL(O) dominates other lines -- it has the best risk/return or the largest slope Slope = (E(R) - Rf) / s [ E(RP) - Rf) / s P ] > [E(RA) - Rf) / sA] Regardless of risk preferences combinations of O & F dominate

104 Figure 6.6 Optimal Capital Allocation Line for Bonds, Stocks and T-Bills

105 Figure 6.7 The Complete Portfolio

106 Figure 6.8 The Complete Portfolio – Solution to the Asset Allocation Problem

107 Extending Concepts to All Securities
The optimal combinations result in lowest level of risk for a given return The optimal trade-off is described as the efficient frontier These portfolios are dominant

108 Figure 6.9 Portfolios Constructed from Three Stocks A, B and C

109 Figure 6.10 The Efficient Frontier of Risky Assets and Individual Assets

110 Exercise 22 1. Adding additional risky assets will generally move the efficient frontier _____ and to the _______. A) up, right B) up, left C) down, right D) down, left 2. Rational risk-averse investors will always prefer portfolios ______________. A) located on the efficient frontier to those located on the capital market line B) located on the capital market line to those located on the efficient frontier C) at or near the minimum variance point on the efficient frontier D) Rational risk-averse investors prefer the risk-free asset to all other asset choices. 1.B 2.B

111 Exercise33 1. The standard deviation of return on investment A is .10 while the standard deviation of return on investment B is If the covariance of returns on A and B is .0030, the correlation coefficient between the returns on A and B is __________. A) .12 B) .36 C) .60 D) .77 2. Consider two perfectly negatively correlated risky securities, A and B. Security A has an expected rate of return of 16% and a standard deviation of return of 20%. B has an expected rate of return 10% and a standard deviation of return of 30%. The weight of security B in the global minimum variance is __________. A) 10% B) 20% C) 40% D) 60% C Ρ = cov(ra,rb)/σa σb = 0.003/(0.10*0.05 )=0.6 2. C WA = [σB2 - Cov(rA, rB)] / (σA2 + σB2 -2Cov(rA, rB)) =[ (0.3)^2-(0.2)(0.3)(-1)]/(0.2^2+0.3^2-2*(0.2)(0.3)(-1)) = 60%, WB =1-WA =40% where Cov(rA, rB) = σA σB ρ

112 Exercise42 1. Which of the following correlations coefficients will produce the least diversification benefit? A) -0.6 B) -1.5 C) 0.0 D) 0.8 2. The expected return of portfolio is 8.9% and the risk free rate is 3.5%. If the portfolio standard deviation is 12.0%, what is the reward to variability ratio of the portfolio? A) 0.0 B) 0.45 C) 0.74 D) 1.35 1.D 2. B ( )/12 = 0.45

113 Single Factor Model ri = E(Ri) + ßiF + e
ßi = index of a securities’ particular return to the factor F= some macro factor; in this case F is unanticipated movement; F is commonly related to security returns Assumption: a broad market index like the S&P500 is the common factor

114 ( ) ( ) b a r r r r e Single Index Model - = + - + Risk Prem
f i m f i i Risk Prem Market Risk Prem or Index Risk Prem a = the stock’s expected return if the market’s excess return is zero i (rm - rf) = 0 ßi(rm - rf) = the component of return due to movements in the market index ei = firm specific component, not due to market movements

115 Risk Premium Format Let: Ri = (ri - rf) Risk premium format
Rm = (rm - rf) Risk premium format Ri = ai + ßi(Rm) + ei

116 Figure 6.11 Scatter Diagram for Dell

117 Figure 6.12 Various Scatter Diagrams

118 Components of Risk Market or systematic risk: risk related to the macro economic factor or market index Unsystematic or firm specific risk: risk not related to the macro factor or market index Total risk = Systematic + Unsystematic

119 Measuring Components of Risk
si2 = bi2 sm2 + s2(ei) where; si2 = total variance bi2 sm2 = systematic variance s2(ei) = unsystematic variance

120 Examining Percentage of Variance
Total Risk = Systematic Risk + Unsystematic Risk Systematic Risk/Total Risk = r2 ßi2 s m2 / s2 = r2 bi2 sm2 / (bi2 sm2 + s2(ei)) = r2

121 Ch 7 Capital asset pricing model and arbitrage pricing model

122 Capital Asset Pricing Model (CAPM)
Equilibrium model that underlies all modern financial theory Derived using principles of diversification with simplified assumptions Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development

123 Assumptions Individual investors are price takers
Single-period investment horizon Investments are limited to traded financial assets No taxes, and transaction costs

124 Assumptions (cont.) Information is costless and available to all investors Investors are rational mean-variance optimizers Homogeneous expectations

125 Resulting Equilibrium Conditions
All investors will hold the same portfolio for risky assets – market portfolio Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value

126 Resulting Equilibrium Conditions (cont.)
Risk premium on the market depends on the average risk aversion of all market participants Risk premium on an individual security is a function of its covariance with the market

127 Figure 7-1 The Efficient Frontier and the Capital Market Line

128 Slope and Market Risk Premium
M = Market portfolio rf = Risk free rate E(rM) - rf = Market risk premium E(rM) - rf = Market price of risk s M

129 Expected Return and Risk on Individual Securities
The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio Individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio

130 Figure 7-2 The Security Market Line and Positive Alpha Stock

131 SML Relationships b = [COV(ri,rm)] / sm2 Slope SML = E(rm) - rf
= market risk premium SML = rf + b[E(rm) - rf]

132 Sample Calculations for SML
E(rm) - rf = .08 rf = .03 bx = 1.25 E(rx) = (.08) = .13 or 13% by = .6 e(ry) = (.08) = .078 or 7.8%

133 Graph of Sample Calculations
E(r) SML Rx=13% .08 Rm=11% Ry=7.8% 3% ß .6 1.0 1.25 ß ß ß y m x

134 Estimating the Index Model
Using historical data on T-bills, S&P 500 and individual securities Regress risk premiums for individual stocks against the risk premiums for the S&P 500 Slope is the beta for the individual stock

135 Table 7-1 Monthly Return Statistics for T-bills, S&P 500 and General Motors

136 Figure 7-3 Cumulative Returns for T-bills, S&P 500 and GM Stock

137 Figure 7-4 Characteristic Line for GM

138 Table 7-2 Security Characteristic Line for GM: Summary Output

139 Multifactor Models Limitations for CAPM
Market Portfolio is not directly observable Research shows that other factors affect returns

140 Fama French Research Returns are related to factors other than market returns Size Book value relative to market value Three factor model better describes returns

141 Table 7-4 Regression Statistics for the Single-index and FF Three-factor Model

142 Arbitrage Pricing Theory
Arbitrage - arises if an investor can construct a zero beta investment portfolio with a return greater than the risk-free rate If two portfolios are mispriced, the investor could buy the low-priced portfolio and sell the high-priced portfolio In efficient markets, profitable arbitrage opportunities will quickly disappear

143 Figure 7-5 Security Line Characteristics

144 APT and CAPM Compared APT applies to well diversified portfolios and not necessarily to individual stocks With APT it is possible for some individual stocks to be mispriced - not lie on the SML APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio APT can be extended to multifactor models

145 Exercise241 1. Stocks A, B, C and D have betas of 1.5, 0.4, 0.9 and 1.7 respectively. What is the beta of an equally weighted portfolio of A, B and C? A) .25 B) .93 C) 1.00 D) 1.13 2. The market portfolio has a beta of __________. A) -1.0 B) 0 C) 0.5 D) 1.0 3. According to the capital asset pricing model, a well-diversified portfolio's rate of return is a function of __________. A) market risk B) unsystematic risk C) unique risk D) reinvestment risk B ( )/3 = 0.93 2. D 1 3.A

146 Exercise 42 1. According to the capital asset pricing model, fairly priced securities have __________. A) negative betas B) positive alphas C) positive betas D) zero alphas 2. Consider the single factor APT. Portfolio A has a beta of 1.3 and an expected return of 21%. Portfolio B has a beta of 0.7 and an expected return of 17%. The risk-free rate of return is 8%. If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio __________ and a long position in portfolio __________. A) A, A B) A, B C) B, A D) B, B 1.D 2.B  Step1, construct a risk free portfolio using portfolio A and B. This risk free portfolio has to have a return as 8% and beta as zero. 0 = WA(1.3)+WB(0.7), WA = -7/6, WB = 13/6, Rp = -7/6(0.21)+(13/6)(0.17) = 12.33% > 8% Step 2, short risk free portfolio and buy risk free asset, therefore you short A and buy B

147 Exercise22 1. Security X has an expected rate of return of 13% and a beta of The risk-free rate is 5% and the market expected rate of return is 15%. According to the capital asset pricing model, security X is __________. A) fairly priced B) overpriced C) underpriced D) None of the above 2. If the simple CAPM is valid, which of the situations below are possible? Consider each situation independently. A) Situation A B) Situation B C) Situation C D) Situation D 1.B ERx = Rf +beta*(Rm-rf) = 5% +1.15*(15%-5%) = 16.5% >13%; It is overvalued. 2.B

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