BU 473 Investment Management
Bruce Everitt
Table of Contents
Asset Classes and Financial Instruments
Real Assets Versus Financial Assets Real Assets Has productive capacity Financial Assets
 Claims on real assets
 Do not directly contribute to productive capacity
 FixedIncome Securities
 Equity
 Derivatives
 Other Investments
 Currency
 Commodity and derivative markets
 Financial Markets and the Economy
 Informational role
 Collective judgment determines stock prices
 Consumption timing
 Separate decisions concerning that otherwise would be imposed by current earnings
 Allocation of risk
 Risk preferences
 Agency Problems
 Tying compensation to stocks
 Monitoring from board of directors
 Monitoring from large investors and security analysts
 Takeover threat for poor performers
 Takeover threat for poor performers Financial Markets
 Money Market
 Shortterm securities (< 1 year)
 Capital markets
 Longterm bond
 Equity markets
 Derivative markets
 The Money Market
 TBill Yields
 Bankdiscount method
 Based on par value (face value) as a denominator and 360 days in a year
 Bondequivalent yield
 Yield is computed based on current price or the purchase price as a denominator and 365 days in a year
 TBill Yields
 Commercial paper
 Bonds issued by highly rated companies Bankers’ Acceptances
 Second only to Tbills in terms of default security
 Canadian Dealer Offered Rate (CDOR)
 Bank guarantees that the debt obligation will be fulfilled
 InflationProtected Bonds – TIPS or RRB
 Taxable vs. TaxExempt Bonds
r * (1t) > rm
 rm: municipal bond rate Corporate Bonds
 Semiannual interest payments
 Callable
 Issuer can exercise the call option to buy the bond back
 Poisoned put
 Forces takeover to buy the bond
 Retractable and extendible
 Modifying the maturity date
 Convertible
 Bond holder can convert bond to equity
 Common Stock eQuity
 Residual claim
 Limited liability
 Dividend yield
 Annual dividend / stock price as a percent
 Capital Gains
 P – C
PE ratio
What is should be versus what it is. Payout ratio over (ke – g). Or (1 retention ratio) / (ke – g) = (1r)/(k_f+β(mrp)g)
Sustainable growth: based on what is retained, times the return on earnings?
ROE = Earnings / Book Value
Preferred Stocks
Cumulative means that missed payments are still owed. With noncumulative preferred shares, company does not have to pay the missed payments ever.
Shares become voting at default payment to preferred shares

Income Trusts
 Usually stable revenues

ADR
 American Depository Receipts
 Trade foreign companies within the USA

Indexes
 S&P/TSX
 S&P/TSX 60 Index
 S&P/TSX MidCap and SmallCap
 S&P/TSX Venture Index

The DOW is priceweighted (not value weighted) and it’s divisor accounts for stocksplits
 priceweighted is where you take the sum of prices and divided it by a divisor (given)
 the return of a priceweighted index is based of the index and not the individual returns

Futures vs. Options
 Future: obligation, option: right
Securities Trading
How Firms Issue Securities
 Prospectus
 Preliminary registration statement filed with the Securities and Exchange Commission
 Initial Public Offerings
 The primary market is where new securities are issued for the first time, while the secondary market is where previously issued securities are traded between investors.
 Road show to publicize new offering
 Bookbuilding to determine demand
 Degree of investor interest provides valuable pricing information
 Underwriter bears price risk
 IPOs are commonly underpriced
 Some IPOs are well overpriced
 Facebook
 Retail investor interest lasts only for 2 days. Institutions always drive volume
 Facebook
 IPOs are commonly underpriced
overallotment: when all equity is sold so banks want more to sell
underwriter takes the risk
Types of Orders
 Market order: buy or sell
 pricecontingent order:
 Limit buy (sell) order to buy at below (above) specified price
 large order filled at multiple prices
Trading Strategies
 Algorithmic trading
 Highfrequency trading
 HIgh volume low profit
 Dark pools
 private trading systems in which participants can buy or sell large blocks of securities without showing their hand
Trading Costs
 Explicit cost
 Commission
 Implicit costs
 Dealer’s bidask spread
 Price concession an investor may be forced to make for big quantities
 Buying board lots is prioritized than fractional
Trading with Margin and Short Sales

Margin is collateral that is on the brokerage platform
 total funds is the collateral (equity) plus the debt

Initial margin is usually 50%
 Maintenance margin
 When equity is 30%, add more money
 How far can a stock price fall before a margin call?

P = Purchase Price * (1  initial margin) / (1  maintenance margin)

P =(Sell Price * (1 + initial margin)) / (1 + maintenance margin)

equity required = initial margin * value  value + borrowed = 1,800

equity total required = 0.6 * value
Leverage
Multiplier effect
Short Sale
Benefit when price goes down.
Insider Trading
 Someone trading on information not profitable
 Most common is spouse of someone on legal team
Debt Yields
 Bank Discount Yield
 Discount / Face Value * 360 / Maturity Days
 Price based on a bank discount yield
 Face value  face value * yield * (days / 360)
 If based on a bond yield, use 365 days
 Holding period return
 The delta you get back divided by the price you paid for it
 Effective annual yield
 The holding period return but compounded to a year (365)
 Suppose a holding period return is 3% for 90 days, what is the effective annual yield?
 (1 + 0.03) ^ (365 / 91)  1 = 12.59%
 Bond equivalent yield
 Ignore effect of compounding (multiply annual holding period return)
 365 day yield but linear instead of compounded
 Holding period return linearly increased to a year
 yield = 3% / (90 / 365)
 Current yield
 Coupon Payment / Price
Questions
A tbill has a bank discount yield of 6.81% based on the ask price and 6.9% based on the bid price. The maturity of the bill is 60 days. Find the bid and ask prices of the bill.
Convert 6.81% and 6.9% for 60 days. 360 days in a year
 1000  1000 * 0.0681 * 60 / 360 = 988.65
 1000  1000 * 0.069 * 60 / 360 = 988.5
 Therefore the bidask spread is just $0.15
A u.s. treasury bill with 90day maturity sells at a bank discount yield of 3%.
 a. what is the price of the bill?
 b. what is the 90day holding period return of the bill?
 c. what is the bondequivalent yield of the bill?
 d. what is the effective annual yield of the bill
answer
 a. 1000  1000 * 0.03 * 90 / 360 = 992.5
 b. 1000 / 992.5  1= 0.756%
 c. 365 days instead of 360: yield = 0.756% * 365 / 90 = 3.06%
 d. 1.00756 ** (365/90)  1 = 3.1%
Purchase 300 shares of GameStart at $40/share. Borrows $4,000 from her broker to help pay for the purchase. Interest rate on loan is 8%.
a. What is the margin of Dei’s account when she first purchases the stock? b. share price falls to $30 per share at year end, what is the remaining margin (equity) on the account? c. margin requirement is 30%, will a margin call occur? d. What is the rate of return?
answer
a. (300 * 40  4,000) / 300 * 40 = (12,000  4,000) / 12,000 = 66.7% b. 30 * 300  4,000 * 1.08 = 4,680 c. 4680 / 9000 = 52% > 30%, so no d. (4680  8000) / 8000 = 41.50%
Short sell 1000 shares of GameStart at $40 per share. Initial margin was 50%. Price rose $10. Stock paid dividend of $2.
a. What is remaining margin? b. 30% margin requirement c. rate of return?
answer
a. Initial equity is 50% * 40,000 = 20,000. Final equity is 20,000 + (40  50  2) * 1000 = 8,000 b. 8000 / (50 * 1000) = 16%, so yes c. (8000  20000) / 20000 = 60%
Consider the following limit order. The last trade was at $50.
….
a. market buy for 200 shares, what price will it be filled at? b. at what price would the next market order be filled?
Investment Companies
 Mutual funds
 Record keeping and administration
 Pool everyone’s money and invest
 Professional management
 Lower transaction costs
 Net Asset Value (market value  liabilities over shares outstanding)
 Unit investment trusts
 REITS
 Real Estate Investment Trusts
 Hedge funds
 Private investors pool assets to be invested by fund managers
 Closedend funds
 Do not redeem or issue shares
 Constant shares outstanding
 Investors cash out by selling to new investors
 Priced at premium or discount to NAV
 Openend
 Stand ready to redeem or issue shares at NAV
 Priced at Net Asset Value
 NAVn = NAV_0[(1 + r)(1  MER)]^n
 Management Expense Ratio
Mutual Fund Investment Policy
 Money market funds
 Invest in money market securities such as commercial paper, repurchase agreements, or CDs
 Equity funds
 Invest primarily in stock
 Sector funds
 Concentrate on a particular industry or country
 Bond funds
 Specialize in the fixedincome sector
 International funds
 Global and emerging market
 Balanced funds
 Designed to eb candidates for an individual’s entire investment portfolio
 Asset allocation and flexible funds
 Hold both stocks and bonds
 Engaged in market timing; not lowrisk
 Index funds
 Tries to match the performance of a broad market index
 Liquid alternatives
 ESG funds
 screened against environmental, social, and governance factors
Fee Structure:
 Management Fees and Operating Expenses
 Frontend load
 Backend load
 Trailing Commissions
Exchange Traded Funds
 Mirrors an index
 Trades like a stock
 Lower costs
 Tax efficiency
Hedge Fund Strategies
 Directional
 Bets that one sector or another will outperform other sectors
 Nondirectional
 Buy one type and sell another
 market neutral
 Statistical arbitrage
 etc
HighFrequency Strategies
 Electronic news feeds
 Crossmarket arbitrage
 Electronic market making
 Electronic “front running”
Examples
 An openend fund has a net asset value of $10.70 per share. It is sold with a frontend load of 6%. What is the offering price?
 $10.70 after offering price, so offering price = 10.70 / 0.094 = 11.38

The offering price is 12.30 with a frontend load of 5%. What is the NAV? NAV = 12.30 * 0.95 = $11.69

You purchased 1,000 shares at $20 with a frontend load of 4%. Securities increased in value by 12%. There is a 1.2% expense ratio. What is the rate of return?
OFF = 20 / 0.96 = 20.83
Final value = 20 * 1.12 * (1  0.012) = 22.13
Rate of return = 22.13 / 20.83  1 = 6.24%
 Loadedup fund has an expense ratio of 1.75%. Economy Fund has a frontend load of 2% but an expense ratio of 0.25%. Assume rate of return is 6% before any fees.
 LU = 1000 * 1.06 * (1  0.0175) = 1041.45 → 4.1%
 EF = 1000 * (1  0.98) * 1.06 * (1  0.0025) = 1036.20 → 3.62%
Risk & Return
 Rate of return on zerocoupon bond; r = (100/Price)  1
 r = (FV/PV)^(1/m)  1
 Annual Percentage (Posted) Rate (APR)
 Effective annual rate (EAR):
 Takes into consideration the effects of compounding
 (1 + APR/n)^n  1
 Example
 APR of 4.5%, m = 4
 100((1 + 0.045/4)^4  1) = 4.58%
 What if you want 4.58%?
 Bank A: 4.58% APR, m = 1
 Bank B: 4.5%, m = 4
 Bank C: APR if compound is 12?
 12 * (1.0458 ^ (1/12)  1) = 4.4867%
 Continuous compounding
 FV = euler’s constant ^ (rt)
 For a EAR of 4.58%, ln (1 + 4.58%) = r → r = 4.475%
Interest Rates and Inflation Rates
 Nominal rate is the growth of your money = 11.5%
 Next year, you get 1.115
 Coffee is $1 today, but given an Average annual rate of inflation of 3.5%, the coffee will be 1.035.
 You could buy 1 coffee now and 1.077 next year
 Change in purchasing power (PP) = 1.077 / 1  1 = 7.7%
 Fisher equation: N approxEqal to real return + inflation
 Equilibrium rate of return
RIsk and Risk Premium
 Holding Period Return = (enter price  enter price + dividend) / (enter price) = Capital Gain Yield + Dividend Yield
 E(r) = sum of probability of state + return if state occurs
 Variance:
 Standard Deviation (STD)
State  Prob. of State  r in State  Weighted r  Var 

Excellent  .25  0.3100  (25)(.31)  (3.1%  9.76%)^ (.25) 
Good  .45  0.1400  (.45)(.14)  (14%  9.76%)^ (.45) 
Poor  .25  0.0675  (.25)(0.0675)  (6.75%  9.76%)^ (.25) 
Crash  .05  0.5200  (.05)(.52)  (5%  9.76%)^ (.05) 
Total  1  N/A  9.76%  0.038 

STD = sqrt(0.038) = 19.49%

Based on a normal distribution, we can expect a return of 9.76% + 19.49% 68% of the time.

Risk: likelihood of something happening and magnitude

STD gives us both the magnitude and the likelihood

Look at historical returns, and calculate the STD of those returns to get the

Skewness: positively skewed means a tail on the right

Kurtosis: how normally distributed data is (fatness of the curve)
Calculating the STD of a Stock Tutorial
 Download monthly data for 5 years from yahoo finance
 Keep only date and adjusted Close columns. Adjusted close factors dividends.
 Make a column called r and use the formula (=X4/X31)
 Calculate average of the rates
 Create a column called variance and use the formula (=(X3  $AVERAGE$RATE)^2)
 Or use the VAR formula in Excel
 Calculate the variance which is the SUM of the column divided by the number of rates MINUS 1
 In a sample, 1 is subtracted to remove the bias to the mean
 Square root the variance to ge the standard deviation of the monthly return
 You can skip the manual calculations and use the VAR and STD formulas provide by Excel.
 You can get the SKEW of the data by using the SKEW function on the returns
 Manually calculating the SKEW
 Create a column and instead of squaring the deviation, cube it
 Divide by the number of rates MINUS 1, and then multiply by the standard deviation cubed
 Use =KURT to get the kurtosis of the rates
 3 is NORMAL
 The lowe the Kurtosis the tighter in the middle
Risk Measures
 Value at risk
 Loss that will be incurred in the event of an extreme adverse price change change with some given, usually low, probability. Typically, use 1st percentile
 2.33 STD
 9.76  2.33 * 19.49 = 35.65%
 Expected Shortfall (ES)
 Lower partial standard deviation (LPSD)
Capital Allocation
 Riskaverse investors consider only riskfree or speculative prospects with positive risk premiums
 Portfolio is more attractive when its expected return is higher, and its risk is lower
 what happens when risk increases along with return
Utility Values
 U = Utility Value
 E(r) = Expected return
 A = Index of the investor’s risk aversion
 Variance of returns
 Scaling factor of 0.5 (half year)
Investor Types
 Riskaverse: want compensation for risk via a premium. A > 0;
 Riskneutral; A =0
 Risklovers; A < 0
MeanVariance Criterion
 E(rA) >= E(rB)
 STD_A <= STD_B
Capital Allocation Across Risky and RiskFree Portfolios
 Manipulate the % invested in riskfree vs risk portfolio
Total market value: $300,000, riskfree: $90,000.
 Equities: 113,400
 Bonds: 96,600
90 day Tbill is considered the riskfree asset.
One Risky Asset and a RiskFree Asset Portfolios
 Rewardtovolatility ratio (aka Sharpe ratio)
 Excess return vs. portfolio standard deviation
 Finding weight based on risk appetite
Indifference curves + Capital Allocation Line
To find the weighting to invest in the risky and riskfree portfolio.
Now we get optimal allocation for any portfolio.
Diversification and Portfolio Risk
 Market risk
 Marketwide risk source
 Remains even after diversification
 Also called systemic or nondiversifiable
 Firmspecific risk
 Risk that can be eliminated by diversification
 Also called nonsystematic risk
Standard deviation cannot drop below a certain line due to market risk. Portfolio risk could be reduced to only 19.2%. At 20 stocks, the marginal benefit is very small. Between 2040 securities, the marginal benefit is needless.
Two Risky Assets
 Covariance of two assets = correlation * stdD * stdE
 Variance of portfolio’s rate of return
State  Prob. of State  r D  r E  COV(rD, RE) 

B  25%  2%  5%  .25*(2% E(rd)) (5%  E(re)) 
N  50%  5%  15%  .25*(5% E(rd)) (15%  E(re)) 
G  25%  8%  30%  .25*(8% E(rd)) (30%  E(re)) 
Total  1  E(rd)  E(re)  Cov(rd, re) 
You need to covariance or the correlation to find the standard deviation.
 pDE = COV(Rd, re) / (rD * rE)
 1.0 <= p <= 1.0
 no diversification if pDE = 1
 if pDE = 1, you can get the weights using wE = stdD / (stdD + stdE) = 1  wD
Graphing Risk
 Straight line between two assets if the correlation is 1
 With perfect hedge (1), there are two straight lines going to risk = 0
 In between, risk is never 0 but a sideways parabola
 Find std for the portfolio for every weighting to get a risk allocation
 Minimum variance portfolio: portfolio allocation with the lowest risk, but not the optimum
 Calculate the slope of all portfolios
 (Expected return of portfolio  risk free rate) / risk of portfolio * A
 A = risk appetite
 Calculate the slope of the capital allocation line
 Tangent portfolio or Optimum portfolio
 Point where the capital allocation line is tangent to the weighting
Minimum Variance Portfolio
Chapter 7 Problems
 Three mutual funds: first is a stock fund, second is a longterm government and corporate bond fund, third is a Tbill fund with 8% yield. The covariance is 0.1 between the two risky funds.
Fund  Expected Return  Standard Deviation  

Stock  20%  30%  (25)(.31) 
Bond  12%  15%  (25)(.31) 
 a. what are the investment proportions in the minimumvariance portfolio
 Using the formula, we get wE =17.39% and wB = 82.61%
 b. what is the expected value and standard deviation of the minimum variance portfolio rate of return
 Expected return is then 13.39%
 Standard deviation (square root of portfolio variance) is then 13.92% (the formula uses covariance)
 c. what are the weights, expected return, and standard deviation of the optimal risky portfolio?
 wB = (Excess return of the bond * rE^2  Excess return of equity * Cov(rE, rB)) / ( excess return of rB * rE^2 + excess return of equity * rB^2  [excess return of B + excess return of E]Cov(rB, rE)) (TODO: turn into latex equation)
 wB = 54.8%, wE = 45.2%
 expected rp = 15.61%
 STD(rp) = 16.54%
 What if you wanted to use the risk free?
 expected return of complete portfolio = 14%
 expected return of complete portfolio = wFrF + wPrP
 14% = (1wp)8% + wp15.61%
 14% = 8% + wp (15.61%  8%)
 wp = (0.14  0.08) / (0.1561  0.08)
 wp = 0.7884
Capital Asset Pricing Model (CAPM)
 Securities Market Line represents beta (risk) vs. return
 Capital Allocation Line becomes Capital Market Line
kinked capital allocation line: when borrowing rate is different (higher) than lending rate
Assumptions
 Individual behaviour
 Investors are rational, meanvariance optimizers
 Their common planning horizon is a single period (holding period is the same)
 Investors all use identical input lists, (homogenous expectations). Publicly available information.
 Market structure
 Price takers
 Publicly held and public exchanges
 Investors can borrow or lend at a common riskfree rate, and they can take short positions on traded securities
 No taxes
 No transaction costs
The Market Portfolio

Market weighted all securities (proxy = SP500 index)

Beta is the correlation with the market risk

Required return of a stock = risk free + beta of the stock times the excess return of the market

Beta = slope of the line of best fit or COV(individual, market) / variance of the market

required return goes up when a stock is sold because of the dividend discount model (dividend yield increases)

alpha is the difference between actual return and required return

track alpha in order to determine if the model is actually working or not
Extensions of the CAPM
 Identical input lists
 ZErobeta model
 Labour income and other nontraded assets
Chapter 9 Problems
 What must be the beta of a portfolio with expected return of a portfolio of 18%, if risk free is 6% and expected market return is 14%?
Beta = (18%  6%) / (14%  6%) = 1.5

Tbill rate is 4%, market risk premium is 6%. What is the fair return?
 $1 Discount store: 12% forecasted, 8% std, beta = 1.5
 Fair return is 4% + 1.5 * 6% = 13%
 Everything $5: 11% expected, 10%, beta is 1.0
 Fair return is 10%
 $1 Discount store: 12% forecasted, 8% std, beta = 1.5
Scenario  Market Return  Aggressive Stock  Defensive Stock 

A  5%  2%  6% 
B  25%  38%  12% 
What are the betas? Use rise over run to calculate the slope using the two scenarios as data points.  (38  (2)) / (25  5) = 2  (12  6)(25  5) = 6/20
What is the expected return on each stock if market returns are equally likely?  Give each scenario a 50% weighting
If the Tbill is 6%, and the market return is equally likely the be 5% 25%, draw the SML for this economy.  E(rm) = 15%  Draw a line from 6% to 25% when Beta is 1
Plot the two securities on the SML graph. What are the alphas of each? Characterize each company in the above table as underpriced, overpriced, or properly priced.  alpha is .3% for the defensive, 6% for the aggressive
Assignment 2
 Outline strategy
 Actively managed
 Must have to modify at least twice
 Propose modifications
Arbitrage Pricing Theory and Factor Models
 APT developed by Stephen Ross
 Exploitation of mispricing for riskfree profits
 Profit has to be made instantaneously and future profit should be 0
 80s, 2 second window
 today, 1/20th of a second
 welldiversified portfolios
 cannot rule out violation of the expected returnbeta relationship for any particular asset
 does not assume mean variance optimizers
 uses an observable market index
Factors of MOdels of Security Returns
 Excess Return (Ri) = E(Ri) + Beta(iIR) + IR + ei + B(iGDP)
 Betai = Factor sensitivity or factor loading or factor beta
 F = Surprise in macroeconomic factor (F could be positive or negative but has expected value of zero)
 ei = Firm specific events (zero expected value)
Factor Models of Security Returns (continued)
 Extra market sources of risk may arise from several sources
Different Expected Returns for Same Risk
Example on slide 13.
If C is below SML and D is on SML, what do you do?
 Bp = .5 = wfBf + waBa
 Bp = .5 = wf(0) + wa(1)
 Therefore, 50% weights
Want to ensure that future value profit is $0 by selling and buying today.
Multifactor APT
FamaFrench Three Factor Model
 Slide 17
 Expansion of CAPM
 Size matters
Performance
DollarWeighted Return (IRR)
Multiperiod Returns
 0: 50
 1: 52
 1: $2 from initial purchase
 4: $4 dividend, sell both shares at $52/share
50 = 51/(1 + r)^2 + 112/(1+r)^2
TimeWeighted Return
r1 = (53  50 + 2)/50 = 10%
r2 = (54  52 + 2)/53 = 5.66%
rg = (1.1 * 1.0566)^(0.5)  1 = 7.81%
True picture of what occurred. Ethical standard.
Adjust Returns for Risk
 Compare rates of return with those of other investment funds with similar risk characteristics
 Comparison universe
 Sharpe Ratio (reward to volatility)
 Treynor Measure
 Average return  Average risk free divided by weighted average Beta for portfolio
 Jensen’s Measure
 ap = rp  \r[rf + Bp(rm  rf)]
 M^{2}
 Leah Modigliani and her grandfather Franco Modigliani
 mix active portfolio with treasury bills until standard deviation equals that of the index the portfolio is being compared to
 If active portfolio has 1.5 times the standard deviation, add 1/3 bills and 2/3 active portfolio (or .5/1.5 in bills and 1/1.5 in portfolio)
 The M2 value is the riskadjusted return minus the index return
 Information Ratio
 alpha / (nonsystematic risk)
Efficient Markets
 prices fully reflect available information
Forms
 Weakform efficiency.
 Semistrong efficiency.
 Strongform efficiency.
Random Walks
 prices are just as likely to go up or down
Insider Information and Cumulative Abnormal Returns
 Food for though. Instead of trading in information, can we predict which company will have news that come out?
CNBC Reports
 midday reports
 positive news already has upticks before release
 negative news has some downticks, but will continue
 does not mean CNBC was first to give the news, but the graph was + 15 minutes
Competition as Source of Efficiency
 information
 Precious
 Strong competition assures prices reflect information
 Higher investment returns motivates informationgathering
 Diminutive marginal returns on research activity suggest only managers of the largest portfolios will find it useful pursuing
Technical Analysis
Fundamental Analysis
 Assess form value that focuses on such determinants as earnings and dividends prospects, expectations for future interest rates, and risk evaluation
 EMH predicts doomed to fail because price reflects available information
 Therefore, analyze information differently than others
Active vs Passive Management
 Active Management
 Expensive strategy
 Suitable only for very large portfolios
 Passive Management
 No attempt to outsmart the market
 Accept EMH
 Index Funds and ETFs
 Lowcost strategy
 Rebalancing
 When new stocks enter or old one leaves
 When there is excess cash like dividends
Event Studies
 Friendly Takeover
 Acquirer has 3%
 +6% for acquired
 Hostile
 Acquirer has +3%
 +20% for acquired
Many researchers have used a market model to estimate abnormal returns.
rt = a + b * rmt + et

rt: stock return

rmt: market rate of return

et: firmspecific events return

b: sensitivity to market return

a: average rate of return if market returns 0

et = rt  (a + brmt)

stock’s return over and above prediction based on broad market movements

Expected Return vs. Abnormal Return
Suppose that the analyst has estimated that a = .05% and b = .8. On a day that the market goes up by 1%, you would predict from Equation 11.1 that the stock should rise by an expected value of .05% + .8 x 1% = .85%. If the stock actually rises by 2%, the analyst would infer that firmspecific news that day caused an additional stock return of 2%  .85% = 1.15%. This is the abnormal return for the day.
Are Markets Efficient?
 Magnitude issue
 Select bias
 Lucky event
WeakForm Tests
 Returns over short horizons
 momentum effect
 continues abnormal performance
 returns over long horizons
 reversal effect is the tendency of return to the proper pricing
PostEarnings Announcement Price Drift
 109 has positive drift
 < 4 has negative drift
Anomalies
 Booktomarket
 Book value divided by market value
 P/E effect
 lowP/E provide higher returns
 Only works on growth companies though
 Good long term fund strategy
 20 lowest y/y revenue growth
 lowP/E provide higher returns
 Neglectedfirm effect
 lesser known firms have generated abnormal returns
 Liquidity effect
 Illiquid stocks have a strong tendency to exhibit abnormally high returns
Behavioural Finance and Technical Analysis
Conventional Finance
 Prices are correct and equal to intrinsic value
 Resources are allocated efficiently
 Consistent with Efficient Market Hypothesis
Behavioural Finance
 Irrational investors
 Arbitrageurs are limited and therefore insufficient to force prices to match intrinsic value
Behavioural Biases
 Framing
 Potential gains from low baseline levels
 Mental accounting
 Segregation of certain decisions
Mental accounting effects also can help explain momentum in stock prices. The house money effect refers to gamblers’ greater willingness to accept new bets if they currently are ahead. They think of (i.e., frame) the bet as being made with their “win nings account,” that is, with the casino’s and not with their own money, and thus are more willing to accept risk. Analogously, after a stock market runup, individuals may view investments as large ly funded out of a “capital gains account,” become more toler ant of ris k, discount future cash flows at a lower rate, and thus further push up prices.
 Regret avoidance
 Regret unconventional decisions more
 Affect and feelings
 Investors choosing stocks that matter to them more which drives up prices and drives down returns
Technical
20day moving average
Relative strength index
Security Price / Industry Price Index
Bollinger band
Breath: spread between number of stocks that advance and decline in prices. If advanced are outnumber declines, market is seen as stronger.
Sentiment Indicators
Confidence Index
 Average yield on 10 toprated corporate bonds divided by the average yield on 10 intermediategrade corporate bonds.
 Ratio will always be below 1, because intermediategrade bonds are riskier than toprated bonds.
 Higher values are bullish since it indicates that intermediategrade bonds are less relatively risky
Short interest

shares short over shares outstanding

share ratio = shares short / daily average trading volume
Put/Call Ratio
 Ratio of outstanding put options over outstanding call options
 Rising ratio taken as a sign of broad investor pessimism
It is possible to perceive patterns that really don’t exist
Trin Ratio
Ratios above 1.0 are considered bearish because the falling stocks would then have higher average volume than the advancing stocks, indicating net selling pressure..
 Data mining
Bonds
 borrowing arrangement
 par value (Face value) paid at the maturity date
 coupon rate (interest payment per dollar of par value)
 bond indenture (the contract between issuer and borrower)
Treasury Bonds and Notes
 Notes: 1 to 10 years
 Bonds: 10 to 30 years
 May be purchased directly from teh Treasury
 $100 to $1,000
Accrued Interest and Quoted Bond Price
 bond prices that are quoted on financial pages are not actually the prices that investors pay
 quoted price is flat price
 invoice or total price paid is called the dirty price
 A semiannual coupon bond with 8% coupon rate
 Days passed since last coupon payment is 30
 Accrued interest = $80/2 * (30/182.5) = 6.58
 coupon rate * par value * (days / 365)
 Invoice = 990 (quoted) + 6.58 = $996.58
Corporate Bonds
 Callable bonds: let’s the issuer buyback the bond
 Convertible bonds: exchange each bond for a specified number of shares of the firm’s stock
 put bond: gives holder option to exchange for par value at some date or extend a number of years
 floatingrate bond has interest rate that is reset periodically according to a specified market rate
Preferred stock
 Promised cash flow stream
 Does not result in bankruptcy
 Dividends owed cumulate
 Rarely gives holders full voting privileges in firm
International Bonds
 Foreign bonds
 Issued by a borrower from a country other than the bond is sold
 Called Maples in Canada, Yankees in the U.S., Samurai bonds in Japan, Bulldog bonds in the U.K.
 Eurobonds
 Denominated in the currency of the borrower but sold in foreign markets
 Not regulated by US
Innovation in the Bond Market
 Inverse floaters are like floatingrate bonds, except coupon rate falls when the general level of interest rates rises
 Assetbacked bonds use income from a specified group of assets to service debt
 Catastrophe bonds (final payment contingent on a catastrophe)
 Indexed bonds are tied to general price index
 Treasury Inflation Protected Securities (TIPS) Indexed Bonds
 The par value of a TIPS bond reflects the change in inflation
 Par value of $1,000 today and inflation of 5% in the year results in a new par value of $1,050
 Canada Real Return Bonds (RRBs)
 Treasury Inflation Protected Securities (TIPS) Indexed Bonds
Bond Pricing
 Coupon / (1 + r)^t + Par value / (1 + r)^T
 Steady: compound periods, maturity date, coupon rate, face value
 Changing: price and yield to maturity
 Price and Face Value
 When price is above face value, coupon rate > yield
 Coupon rate and yield to maturity
 If yield > coupon rate, price is less than face value
 Price and Face Value
What if it weren’t? Then there would be easy profits to be made. For example, if investment dealers ever noticed a bond selling for less than the amount at which the sum of its parts could be sold, they would buy the bond, strip it into standalone zero coupon securities, sell off the stripped cash flows, and profit by the price difference . If the bond were selling for more than the sum of the values of its individual cash fl ows, they would run the process in reverse: buy the individual zerocoupon securities in the STRIPS market, reconstitute (i.e., reassemble) the cash flows into a coupon bond, and se ll the whole bond for more than the cost of the pieces. Bot h bond stripping and bond reconstitution offer opportunities for arbitrage the exploitation of mispricing among two or more securities to clear a riskless economic profi t. Any violation of the Law of One Price, that identical cash flow bundles must sell for identical prices, gives rise to arbitrage opportunities.
Bond Risks
 Default risk
 Interest rate risk
 Price will drop because interest rates rise
 Offset my shorter maturity and higher coupon rate
 Reinvestment risk
 If rates change, the reinvestment yields a different return
Bond Sensitivity to Yields
Bond prices are less sensitive at high interest rates and very volatile at lower interest rates. Around par, a small increase in interest rate will have a large affect on price. Longer dated bonds are more sensitive.
Yield to Maturity Example
8% semiannual coupon, 30year bond, $1,276.76. YTM is not the EAR.
1276.76 = SUM {1..60} 40 / (1 + r)^60 + 1000 / (1 + r)^60
Yield to Call
 low interest rates means price is flat since risk of repurchase is high
 With high interest rates, the price of the callable bond converges to that of a normal bond since the risk of call is negligible
Realized Compound Return vs YTM
 YTM assumes coupons are reinvested at the YTM
 Realized compound return is also a yield but is assumes that coupon payments are reinvested at the reinvestment rate
 Forecasting the realized compound yield over various holding periods or investment horizons is horizon analysis
 Prices of bonds with different coupon rates converge near maturity
 HPR: can only be forecasted
 Investment period
Example
 2year bond selling at par value that pays an annual 10% coupon with a reinvestment rate of 8%
 Future Value = 1,000 + 100 + 100 * 1.08 = 1,208
 Realized compound return: 1,000 * (1 + r)^2 = 1,208
def realized_compound_return(years, price, future_value):
# return (1+r)^years = future_value / price
return (future_value / price) ** (1/years)  1
realized_compound_return(2, 1000, 1208) * 100 # 9.909053312272697
Zero Coupon Bond
Always trades at a discount since no coupon rate
Discriminant Analysis
 Edward Altman used discriminant analysis to predict bankruptcy
 Financial characteristics are used to assign a score
 z = 3.1 (EBIT / Assets) + 1 (Sales / Assets) + 0.42 ( Equity / Liabilities )
 Scores between 1.23 and 2.90 are gray area
 Scores above 2.90 are considered safe
Bond Indentures
 Sinking fund
 calls for the issuer to periodically repurchase some proportion of the outstanding prior to maturity
 Subordination clauses restrict the amount of additional borrowing by the firm
 Dividend restrictions limit the payment of dividends by the firms
 Collateral is a particular asset that the bondholder receive if the firm defaults
Default Risk and YTM
 Promised YTD realized only if the firm meets obligation of the bond issue
 Expected YTD must consider the possibility of a default
 Default premium is a differential
 CCC bond default probability is 34%
Credit default swaps (CDC)
 Insurance policy on the default risk of a bond or a loan
 Allows lenders to buy protection against default risk
 Risk structure of interest rates and CDS prices ought to be tightly aligned
 CDS contracts trade on corporate as well as sovereign debt
Collateralized Debt Obligations (CDO)
 Major mechanism to reallocate credit risk in the fixedincome markets
 Establish a legal entity; Structured Investment Vehicle
 Loans are pooled and split into tranches
 Mortgage backed CDOs were an investment disaster in 20072009
 Obligations found in Slide 14, page 39
Fixed Income Term Structure
Yield Curve
 Zero coupon bond yield plotted to maturity
 inverted yield curve: shortterm rates are higher than longterm
 higher risk for shortterm
 normal yield curve has higher longterm yields
Valuing Coupon Bonds
 Discount based on zerocoupon bond yield for each year
 Find a discount rate (ytm) that equals the future value
 EXCEL:
PV(C85,3*2,50,1000)
import numpy_financial as npf
def coupon_bond_price(period_discount_rate, years, coupon_rate, coupon_freq, par_value=1000):
# period discount_rate: AKA effective compound rate; Tbill yield; zerocoupon bond yield
return npf.pv(period_discount_rate, years * coupon_freq, par_value * coupon_rate / coupon_freq, par_value)
Spot & Forward Rates
A forward rate is just one year period, but spot rates can be multiple. {a = maturity period in years, b = years into the future}. y_{x} = yield for period x.
Mortgage Rates
Can apply to mortgage interest rates as well.
Interest rates can be fixed at 1, 2, 3, etc. By forwarding rates, we can look at the best deal.
What does the 1 year rate need to be 4 years from now, to be indifferent.
Problems:
 liquidity preference theory: forward rate is higher than expected rate
Interpreting the Term Structure
 yield curve reflects expectations of future interest rates
 forecasts are clouded by liquidity premium
 upward sloping curve
 rates are expected to rise or liquidity premium to hold long term bond
 yield predicts business cycle
 longterm rates tend to rise in anticipation of economic expansion
 inverted yield curve may indicate falling interest rates and signal a recession
Interest Rate Sensitivity
Shortterm vs. Longterm
shortterm (2 year)
YTM  Zero  Zero % Change  10% Annual Coupon  Coupon Bond % Change 

11%  811.62  1.8  982.87  1.71 
10%  826.45  N/A  1000  N/A 
9%  841.68  1.8  1017.59  1.76 
Longterm (30y)
YTM  Zero  Zero % Change  10% Annual Coupon  Coupon Bond % Change 

11%  4368  23.8  913.06  8.69 
10%  5731  N/A  1000  N/A 
9%  7537  31.5  1102.74  10.3 
Duration
 Calculate the discounted cash flow for each time a cashflow is received
 Calculate the weights for each discounted cash flow as a percentage of the price (present value)
 Multiply each weight by the period in time (e.g. cash flow in period 2 multiplied by 2)
 Macaulay’s duration is the sum of the timeweighted discounted cash flows in the previous step

weighted each time by the present value of cash flows at each time divided by the price

multiply each weight by the time

duration equals the maturity for a zero coupon bond

duration < maturity of a coupon bond

present value of a cash flow at a time divided by the price

modified duration is the duration discounted by the yield divided by the number of periods in a year
 modified duration goes back a period because of better results

expected price % change = D * (change in interest rate)

assets with the same duration are equally sensitive

divide duration by number of periods in a year
Convexity
 sensitivity is different at each duration
 investors like convexity because bond prices don’t drop as much but can increase in price faster
 Add 0.5 * Convexity * (change in yield)^2
Callable Bonds Duration and Convexity
Intrinsic Value vs. Market Price
If you require a return and the intrinsic value you calculate equal the market value, buy it because it does give you the required return.
 IV > MV → Buy
 IV < MV → Sell
 IV = MV → Buy
Dividend Growth Model
P = D1 / (k  g)
NonLinear Dividend Growth
Discount each dividend back until a far enough period (D6) and discount that by a growth rate.
Present Value of Growth Opportunities
P = E / k + Present Value of Growth Opportunity
P0/E1 = (1  b) / (k  ROE * b)
ROE * b = sustainable growth rate
k = CAPM, b = retention rate, 1  b = payout ratio
Sustainable Growth = b * ROE
Use Dupont ratio to justify the P/E.
Market EV definition = Market Cap + Debt  Cash
Financial Statement Analysis
yoyo: when you say a something went up (not good)
Time analysis:
Why did a ratio go up?
Net Interest Margin
Income Statement Ratios
Gross Profit Margin = Sales  Costs / Sales
EBITDA Margin = Cash Flow Margin
Operating Margin = EBIT / Ssales
Degree of operating leverage ( DOL) = (percentage change in profits) / (percentage change in sales)
Profit Margin = Profit / Sales
TIE = EBIT / Interest
Why change over time. Why different from competitors.
Anomalies:
 government support
Balance Sheet Ratios
 swapping shortterm debt for longterm debt
 possible that accounts receivable spikes due to a big sale
 it went down because you collect faster
 based on liquidity
 Sears took over a year to get rid of inventory
 capital structure
 leverage measure
 could go up because: buyback shares with debt
 just raised debt for long term assets
Return Ratios
Return on Assets
EBIT / Total Assets
Return on Net Assets
EBIT / Net Assets
Return on Capital
EBIT / (Long Term Debt + Equity)
Return on Equity
ROE = NI / S * S / TA * TA / E
Equity Multiplier Leverage
TA / E = (E + D) / E = 1 + D/E
Productivity Ratios
average collection period
AR / Net Credit Sales * 365
Total Asset Turnover
Sales / Total Assets
Inventory turnover
COGS / Inv
Days Inventory
365 / Inventory Turnover
Walmart has a days inventory ratio of ~20.
AR Turnover
Sales / AR
Days S/O
AR / S * 365
Economic Value Added
 Capitla = 1000
 wacc = 5%
 capital charge = 50
 ROC = 75/1000 = 7.5%
 EVA = (75  50) = 25
 (ROC  wacc) * Capital
Price Per Equity
Interest Coverage Ratio
Dividing a company’s earnings before interest and taxes (EBIT) by its interest expense
TODO: use latex
Compound Leverage Ratio = Interest Burden * Leverage
Earnings management
Earnings management is the practice of using flexibility in accounting rules to improve the apparent profitability of the firm. We will have much to say on this topic in the next chapter on interpreting financial statements. A version of earnings management that became common in the 1990s was the reporting of “pro forma earnings” measures.
Options
The Option Contract
 Call Option:
 gives its holder the right to purchase an asset at a specific price
 Put option:
 gives its holder the right to sell an asset at a specific price
 In the money occurs when exercise would produce positive cash flow
 call option strike price < market price
 put option strike price > market price
Call
 x = 60, P = 3
 Buyer
 Payoff: max ( stock price  x, 0)
 Profit: payoff  premium
Put
 x = 60, P = 3
 Buyer
 Payoff: max ( x  stock price, 0)
 Profit: payoff  premium
American vs. European
American options can be exercised at any time whereas European options can only be exercised on the exercise day.
Types of Options
 Index options
 futures options
 foreign currency options
 interest rate options
Exotic Options
 Asian
 Based on average stock price over a time period
 Payoff is the difference between that average and the strike price
 Based on average stock price over a time period
 Barrier
 depends on the price at expiration as well as if the price crossed a barrier
 knockout: if the price falls to a certain extent, the option expires worthless
 knockin: if the price does not fall to a certain extent, the option expires worthless
 Lookback Options
 Depends on the minimum and maximum price of the underlying asset during the life time of the option
 Call option may provide payoff equal to maximum  strike
 Currencytranslated options
 asset or exercise prices denominated in a foreign currency
 quanto: fix exchange rate
 digital options
 fixed payoff if a condition is satisfied
PutCall Parity
 Putcall parity theorem is an equation representing the proper relation between put and call prices
 violation implies arbitrage opportunities
 sell high side, buy low side
 invest cash from sell
Suppose C = 3, P = 3, X = 60, r = 5%, and stock price is 60.
 Sell stock: + 60
 Sell put: + 3
 Buy call 3
 Invest 57.14
 Net: $2.85
In a year or so, the investment becomes $60; You can either buy shares back at 60, your shares get called back at 60 because of the put.
A good “riskfree” asset is CASH.TO
Real example.
Microsoft, 1 year expiry. OTM Call has premium (price) 30.48. Put has a premium of 43.50 with strike of 370. Strike price is 370. riskfree rate is 4%. Stock price is 345.
 30.48 + 370/1.04 = 345 + 43.5
Straddle
A long straddle is established by buying both a call and a put on a stock, each with the same strike price and expiration date.
A straddle is a bet on volatility. The cost of a straddle is the sum of the call and the put, P + C. Final stock price must depart from X by this cost for the straddle to provide a profit.
Strips and straps are variations of the straddle.
Collars
 Examples
 butterfly
 condor
 limited downside
Futures
Similar to options however with futures and forward contract, there is an obligation to follow through with the agreedupon transaction.
 Forward contracts call for future delivery at a currently agreed upon price
 Price holds
 Futures contract obliges traders to purchase or sell an asset at an agreedupon futures price at contract maturity
 Price may fluctuate
 Zerosum game
 Profit is zero when spot price equals the initial futures price
Future Main Concepts
 Marked to market every day
 Maintenance margin
 Convergence property (futures price and spot price converge at maturity)
Strategies
 Speculators
 Bet whether price will go up or down
 Hedgers
 Protect against price movements
 Long: protect against a higher spot price in the future
 Short: protect against spot prices going down in the future
 Calendar spread
 Long position in a futures contract at one maturity and short in another
SpotFutures Parity Theorem
 Violation of the parity relationship gives rise to arbitrage opportunities
 Investor holds $1,000 in a mutual fund for S&P500/TSX Index
 Dividends of $20
 The futures contract with delivery in one year trades for $1,010
 Since delivery doesn’t include the delivery of the dividends, the investor can hedge
A perfect hedge should return the risk less rate of return
Arbitrage
 Parity relationship also is called the costofcarry relationship
 If the futures price is too high, short the futures and acquire the stock by borrowing the money at the riskfree rate
 If the futures price is too low, go long futures, short the stock and invest the proceeds at the riskfree rate
Spreads
When dividends do not exist, spot–futures parity states that the equilibrium futures price:
Futures Prices vs. Expected Spot Price
When spot is unchanged:
 Expectations hypothesis
 Future price = the spot price
 Normal backwardation
 Future prices are less and then meet the spot price
 Contango
 future prices are higher and then fall to spot
 Modern portfolio theory