Investment planning Flashcards
Holding period return (HPR)
(Ending Value-Beginning Value) + Income / Beginning Value
Dividends received: add to numerator
Margin interest paid: subtract from numerator
If question mentions after-tax gain or loss, taxes paid are subtracted from numerator.
When purchasing securities on margin, include only equity in the trade in the denominator.
Forms of Underwriting: Best Efforts
Underwriter agrees to sell as much as possible of the offering, risk of issue not selling resides with firm (unsold shares return to company)
Forms of Underwriting: Firm Commitment
Underwriter agrees to buy entire issuance of stock from the company, may make a spread (e.g., buy for $18 and sell for $20).
Risk that an issuance may not sell stays with the underwriter.
Prospectus
Outlines risks, management team, business operations, fees, and expenses.
Must be issued by investment company prior to selling shares to investor.
Red Herring
Preliminary prospectus issued before SEC approval, used to determine investors’ interest in the security
10K Report
Annual report of financial statements filed with the SEC. 10K is audited.
10Q Report
Quarterly report filed with the SEC - NOT audited
Annual Report
Sent directly to shareholders
Contains message from Chairman of the Board on the progress in the past year and outlook for coming year
Liquidity
How quickly something can be turned into cash, with little or no price concession. Short term investment assets are considered liquid: CDs money market accounts high-yield savings accounts government bonds Treasury bills
Marketability
Exists where there is a ready-made market for something. Marketable investments include: Stocks Bonds Mutual funds Exchange traded funds Treasury Bills Money Market instruments
Market Order
Timing and speed of execution are more important than price
Appropriate for stocks that are not thinly traded
Limit Order
Price at which trade is executed is more important than timing
Most appropriate for stocks that are extremely volatile and are not frequently traded
Stop Order
When the price hits a certain level, the order becomes a market order, stock is sold at that price or lower. Primary risk: investor may receive significantly less than anticipate if market is moving too quickly.
Stop-Limit or Stop-Loss-Limit Order
Investor sets 2 prices:
(1) stop-loss price - once this is reached, the order turns into a limit order
(2) limit price - investor will not sell below the second price
Risk: if market moves quickly, order may not fill and investor will be left with stock at significantly lower price.
Appropriate for investors with a significant gain built into the stock, but who may not want to sell during period of significant volatility.
Short selling
Selling at a higher price, in the hopes of purchasing the stock back at a lower price (goal: sell high, buy low)
Investor makes profit when asset’s price decreases in value.
Must have margin account to protect against appreciation of the stock.
No time limit on how long investor can maintain the short position.
Dividends paid by the company must be covered by the short seller.
Initial Margin
Amount of equity an investor must contribute to enter a margin transaction
Reg T set initial margin at 50% and established by the Federal Reserve
Can be more restrictive based on the volatility of a stock
Assume 50% on the exam unless stated otherwise in the question
Maintenance Margin
Minimum amount of equity required before a margin call
Margin position
Current equity position of the investor
Margin call
Loan / 1 - Maintenance Margin
Sample calculation: How much equity must an investor contribute, when a stock price falls below the stock price and the investor will receive a margin call?
Bob purchased 100 shares of Starbucks trading at $50 per share with an initial requirement of 75% and a maintenance margin of 35%. The price fell below $15. How much equity must Bob contribute?
Required Equity:
Stock price: $15
Maint. Margin: x 0.35
Required Equity: $5.25
Sample calculation: How much equity must an investor contribute, when a stock price falls below the stock price and the investor will receive a margin call?
Bob purchased 100 shares of Starbucks trading at $50 per share with an initial requirement of 75% and a maintenance margin of 35%. The price fell below $15. How much equity must Bob contribute?
Required Equity:
Stock price: $15
Maint. Margin: x 0.35
Required Equity: $5.25
Sample calculation: How much equity must an investor contribute, when a stock price falls below the stock price and the investor will receive a margin call?
Bob purchased 100 shares of Starbucks trading at $50 per share with an initial requirement of 75% and a maintenance margin of 35%. The price fell below $15. How much equity must Bob contribute?
Required Equity Actual Equity
Stock price: $15 Stock Price: $15
Maint. Margin: x 0.35 Debt: $12.50
Required Equity: $5.25 Actual Equity: $2.50
$5.25 - $2.5 = $2.75 per share = $275 in total
Research Reports: Value Line
Ranks STOCKS on a scale of 1 to 5 for timeliness and safety
Ranking of 1 represents the highest ranking for timeliness and safety (signal to buy)
Ranking of 5 represents lowest ranking (signal to sell)
Research Reports: Morningstar
Ranks mutual funds, stocks, and bonds using 1 to 5 stars (primarily MUTUAL FUNDS!)
1 star represents lowest ranking, 5 stars represent highest ranking
Dividend Dates
Dividends are declared by the BOD and typically paid quarterly
Ex-Dividend Date
Date of Record
Ex-Dividend Date
Date the stock trades without a dividend
If you sell the stock on the ex-dividend date, you will receive the dividend
If you buy the stock on or after the ex-dividend date, you will NOT receive the dividend
Ex-dividend is ONE BUSINESS DAY before the date of record
Remember: EX-Date trades without dividend
Date of Record
Date on which you must be a registered shareholder in order to receive the dividend
= ONE BUSINESS DAY after the ex-dividend date
Investor must purchase the stock 2 business days prior to the date of record in order to receive the dividend
Purchases made on ex-dividend date will not receive the dividend; to receive the dividend, an investor must purchase the stock prior to the ex-dividend date or 2 business days before the date of record
Types of Dividends
Cash dividends: Qualified dividends receive capital gains tax treatment
A cash dividend is taxed upon receipt
Stock dividends: not taxable to shareholder until stock is sold
Stock splits
Increase shares and reduce stock price:
2-for-1 split for 100 shares at $50 per share results in 200 shares at $25 per share
3-for-2 split for 100 shares at $60 per share results in 150 shares at $40 per share
Securities Act of 1933
Regulates issuance of new securities (Primary Market) - IPOs
Requires that new issues are accompanied with prospectus before being purchased
Securities Act of 1934
Regulates secondary market and trading of securities
Created SEC to enforce compliance with security regulations and laws
Investment Company Act of 1940
Authorized SEC to regulate investment companies
3 types of investment companies: Open, Closed, UITs
Investment Advisors Act of 1940
Required investment advisors to register with the SEC or state
Securities Investors Protection Act of 1970
Established SPIC to protect investors from losses resulting from brokerage firm failures
Does not protect investors from incompetence or bad investment decisions
Insider Trading and Securities Fraud Enforcement Act of 1988
Defines and insider as anyone with information that is not available to the public
Insiders cannot trade on that information
Money Market Securities
Treasury bills
Commercial paper
Bankers Acceptance
Eurodollars
Treasury Bills
Issued in varying maturities up to 52 weeks
Denominations in $100 increments through Treasury Direct up to $5 million per auction. Larger amounts available through a competitive bid
Commercial paper
Short-term loans between corporations Maturities of 270 days or less Does not have to register with the SEC Denominations of $100,000 Sold at discount
Bankers Acceptance
Facilitates exports/imports
Maturities of 9 months or less
Can be held until maturity or traded
Eurodollars
Deposits in foreign banks that are denominated in US dollars
Investment Policy Statement
Establishes
(a) client’s objectives: required return, risk tolerance
(b) limitations on investment manager (time horizon, liquidity needs, taxes, laws and regulations, circumstances unique to the client)
Used to measure investment manager’s performance
Does NOT include investment selection
Remember: IPS establishes RR TT LL U - risk, return, taxes, timeline, liquidity, legal, unique circumstances
Market Averages and Indices
Dow Jones Industrial Average:
Simple Price-Weighted Average
Does not incorporate market capitalization
S&P 500:
Value-Weighted index
Incorporates market capitalization
Russell 2000:
Value-Weighted index of the smallest capitalization stocks in the Russell 3000
Wilshire 5000:
Broadest Value-Weighted index measuring performance of over 3000 stocks
EAFE:
Value-Weighted index tracking stocks in Europe, Australia, Asia, Far East
Standard Deviation
Measures risk and variability of returns
The higher the SD, the higher the riskiness of the investment
Measures TOTAL RISK of an UNDIVERSIFIED portfolio
Probability of returns: 68% = 1 x SD; 95% = 2 x SD; 99% = 3 x SD (add or subtract to mean return)
Calculating Standard Deviation
Dan has 2 stocks in his portfolio with the following returns over the past 5 years:
A: 10%, 13%, 8%, -2%, 14%
B: 6%, -3%, 4%, -5%, 7%
Calculate the SD for both stocks:
10 Σ+ 13 Σ+ 8 Σ+ 2+/-Σ + 14 Σ, Orange Shift Sx, Sy
6 Σ+ 3+/- Σ+ 4 Σ+ 5+/-Σ + 7 Σ, Orange Shift Sx, Sy
A= 6.3875%
B= 5.4498%
A is more risky because SD is higher
What is the total expected return for the following portfolio?
Expected Return Probability
10% 30%
15% 60%
18% 10%
Answer: 13.80%
10% x 30%) + (15% x 60%) + (18% x 10%
Coefficient of Variation
CV= Standard Deviation / Average Return
Useful in determining which investment has more relative risk when investments have different average returns
Tells us probability of actually experiencing a return close to the average return
The higher the coefficient of variation the more risky an investment per unit of return.
If 2 investments have the same return, go with the higher Standard Deviation to determine the higher risk investment.
Normal Distribution
- used in probability analysis of expected returns around an average return
- average (expected) outcome in the middle X
- symmetrical curve
- 50% probability of a return > X
- 50% probability of a return < X
Standard deviation σ measures variance around that expected return
- probability of a return falling within +/- 1 σ of the average is 68%
- probability of a return falling within +/- 2 σ of the average is 95%
- probability of a return falling within +/- 3 σ of the average is 99%
Lognormal Distribution
appropriate when investor is considering a dollar amount or portfolio value at a point in time
Skewness
Refers to the extent to which a distribution is not symmetrical.
Positively skewed distributions may have outliers in the upper, or right tail (“skewed to the right”)
Stock markets tend to be positively skewed.
Negatively skewed distributions have many outliers in the lower, or left tail (“skewed left”).
Commodity returns tend to be skewed.
Kurtosis
Describes when a distribution is more or less peaked than a normal distribution.
Refers to the variation of returns:
Normal distribution: mesokurtic
Little variation of returns: distribution has high peak = positive kurtosis (Leptokurtosis) - slender (e.g., Treasuries)
Widely dispersed returns: low peak = negative kurtosis (Platykurtosis) - broad
Mean Variance Optimization
Process of adding risky securities to the portfolio but keeping the expected return the same, finding the balance of combining asset classes that provide the lowest variance as measured by standard deviation.
Monte Carlo Simulation
Spreadsheet simulation that gives probabilistic distribution of events occurring, e.g., what is the probability of running out of money in retirement with a client who has a withdrawal rate of 3%, 4%, 5%. Monte Carlo simulation adjusts assumptions and returns the probability of an event occurring depending upon the assumption.
Covariance
measure of 2 securities combined in their interactive risk, i.e., how price movements between the 2 are related to each other
measures relative risk
If correlation coefficient is known, or a given, covariance is calculated as the deviation of investment A times the deviation of investment B times the correlation of investment A to investment B:
COV AB = (σA) (σB) (ρAB)
ρ= correlation coefficient
σ = Standard deviation
Correlation Coefficient
Correlation and Covariance measure movement of one security relative to that of another, both are RELATIVE measures.
ρAB = Cov AB /(σA) (σB)
Correlation ranges from +1 to -1 and provides insight into strength and direction 2 assets move relative to each other:
Correlation of +1 denotes perfectly positive correlation to each other
Correlation of -1 denotes perfectly negative correlation
Correlation of 0 denotes that assets are completely unrelated
Diversification benefits (risk reduced) begin anytime correlation is LESS than 1
Investment Risk - Define:
Risk
Total Risk
Systematic Risk
Unsystematic Risk
Risk = experiencing an outcome different than the expected outcome
Total risk = Systematic + Unsystematic Risk, measured by STANDARD VARIATION
Systematic Risk cannot be eliminated through diversifying the portfolio, measured by BETA
Unsystematic Risk can be eliminated through diversifying the portfolio (aka “firm-specific risk”)
Systematic / Non-diversifiable / Market / Economy based risk - Components
PRIME:
Purchasing Power Risk Reinvestment Risk Interest Rate Risk Market Risk Exchange Rate Risk
Unsystematic / Diversifiable / Unique / Company Specific Risk - Components
ABCDEFG:
Accounting Risk Business Risk Country / Sovereignty Risk Default or Credit Risk Executive Risk Financial Risk Government / Regulation Risk
Risk and Return
The higher the standard variation, the greater the variance around the expected return.
Investments with greater standard deviation (higher risk!) require greater expected return. (e.g.: common and preferred stock, junk bonds, options, futures, forwards, small cap and growth-oriented funds)
Investments with lower standard deviation will typically provide lower returns, but provide limited downside risk. (e.g., cash, MMKT securities, Treasury securities, investment grade bonds)
Factors influencing investor’s capacity for risk
Time horizoin
Liquidity needs
Total investable assets
Risk/Return Relationship
Potential return and Risk in order from LOW to HIGH:
Treasury Bills (cash alternatives) CDs (cash alternatives) Government Bonds Corporate Bonds Preferred Stocks Common Stocks Options & Futures
Beta Coefficient
= measure of systematic (market) risk
measures individual security’s volatility relative to that of the market
best used to measure volatility of a diversified portfolio (one that has a high r2
Beta of the market = 1
Stock with Beta of 1 is expected to mirror the market in terms of direction, return, and fluctuation
Stock with a Beta >1 means it fluctuates more than the market, and greater risk is associated with that security
Stock with a Beta <1 indicates it fluctuates less relative to market movements.
→ The greater the Beta Coefficient of a security, the greater the systematic risk associated with that security.
NOTE: The BETA of an INDEX Fund is always 1 because it tracks the market!
Calculation of Beta
βi = COVim / σ²m = (ρim) (σ) / σm
COVim = (σi) (σm) (ρim) σ²m = Variance of the market σm = SD of the market σi = SD of the individual security ρim = correlation coefficient between individual security and market
Beta can also be calculated in the following way:
Security risk premium / Market Risk premium
Example: If a fund has a return of 20% and the market has a return of 10%, the beta would be 20 / 10 = 2.
If a fund has a return of 5% and the market has a return of 10%, the beta would be 5 / 10 = 0.5.
Coefficient of Determination - R-Squared (r2)
measures what percentage of a security’s return is due to the market
Calculate Coefficient of Determination by squaring correlation coefficient :
Example: If mutual fund XYZ has a correlation coefficient of 0.80, its coefficient of determination is 0.64, which means 64% of the fund’s return is due to the market.
R-squared also provides insight into how well-diversified a portfolio is: the higher R-squared, the higher percentage of return from the market (systematic risk) and less from unsystematic risk.
R-squared tells the investor if Beta is an appropriate measure of risk: if R-squared ≥ 0.70, Beta is an appropriate measure of total risk. If R-squared ≤ 0.70, use Standard Deviation instead to measure total risk.
Sample Calculation Correlation of Determination
Mutual Fund XYZ has a 5-year return of 12%, with a standard deviation of 15%. Fund XYZ has a Beta of 1.4 with a correlation of 0.90 to the S&P 500. What percent of the return from Fund XYZ is due to the S&P 500?
a) 90%
b) 81%
c) 19%
d) 10%
81% - answer B: 0.90 = r, thus R-squared = 0.81 or 81%. 81% is due to the market, and 19% is due to unsystematic risk.
A mutual fund has a correlation coefficient of 0.80. What percent of return is due to unsystematic risk?
R Squared = 0.64 or 64% is due to systematic risk, thus 36% is due to unsystematic risk!
Portfolio Risk
Can be measured through determination of the interactivity of the standard deviation and covariance of securities in the portfolio.
“Portfolio Deviation Formula” or “Standard Deviation of a Two Asset Portfolio” utilizes the weight of both securities involved, the deviations of the respective securities, and the correlation coefficient of the two securities
(see Formula sheet)
Alternative possibility:
Take simple weighted average of the standard deviation of a portfolio, then choose the answer that is the next lower one than the average (e.g., SD 10.5% and 23.8%, equal weight of 50% → (10.5x 50) + (23.8x50) = 17.5%
Answer choices: 10.8%, 13.7%, 18.45, 20.5% → choose 13.7%
Modern Portfolio Theory
Acceptance by an investor of a given level of risk while maximizing expected return objectives.
When designing a portfolio the most important variables are risk, return and covariance (how asset classes relate to each other).
Negatively correlated assets are not necessary to reduce risk, simply assets with a correlation < 1 are necessary.
Diversifying across asset types is more effective by combining stocks and bonds.
The efficient frontier is very sensitive to the risk and return input variables.
Efficient Frontier
Curve illustrates optimal amount of return for a unit of risk taken.
Uses standard deviation for risk measure.
All points on the efficient frontier are deemed equally efficient.
Where you plot on the curve is determined by risk tolerance.
Portfolios below the efficient frontier are inefficient because there is a portfolio that provides more return for that level of risk.
Area above the efficient frontier is considered unattainable.
Efficient Portfolio
Occurs when an investor’s indifference curve is tangent to the efficient frontier.
Indifference curves
Constructed using selections made based on highest level of return given an acceptable level of risk.
Risk averse investor will have steep indifference curve. This investor requires significantly more return to take on just a little more risk.
A risk tolerant investor will have a flat indifference curve. This investor will not require a significant amount of return to take on more risk.
Optimal Porfolio
The one selected from all efficient portfolios: the point at which an investor’s indifference curve is tangent to the efficient frontier represents the investor’s optimal portfolio.
Investors seek the highest return attainable at any level of risk.
Investors want the lowest level of risk at any level of return.
Investors are assumed to be risk-averse.
Capital Market Line - CML
Macro aspect of the Capital Asset Pricing Model (CAPM)
Specifies the relationship between risk and return in all possible portfolios.
CML becomes the new efficient frontier, mixing in the risk-free asset with a diversified portfolio.
A portfolio’s returns should be on the CML.
Inefficient portfolios are below the CML.
CML is NOT used to evaluate performance of a single security.
CML uses STANDARD DEVIATION to measure risk.
Rp =rf + σp (rm - rf) / σm
where:
Rp = portfolio return
rf = risk free rate
σp = standard deviation of portfolio returns
rm = market return
σm = standard deviation of market returns
Capital Asset Pricing Model (CAPM)
Calculates the relationship of risk and return of an individual security using Beta as its measure for risk.
Often referred to as the Security Market Line (SML) equation because its inputs and results are used to construct the SML.
The difference between (rm - rf) is considered the market risk premium, i.e., how much an investor should be compensated to take on a market portfolio vs. a risk-free asset.
- quantifies expected return
- quantifies required ROR
- plots the SML
ri = rf + (rm - rf) βi
ri = required or expected ROR rf = risk free ROR βi = Beta, systematic risk of the portfolio rm = return of the market rm - rf = market risk premium
Exam tip: sometimes the market risk premium will be given rather than the return of the market.
stock premium = (rm - rf) βi
Security Market Line (SML)
The relationship between risk and return as defined by the CAPM and graphically plotted results in the SML.
Both the CAPM and the SML assume an investor should at least earn a ROR equal to the risk-free rate of return.
The SML intersects the y-axis at the risk-free rate of return.
SML uses BETA to measure risk, CML uses SD to measure risk.
If a portfolio provides a return ABOVE the SML, it would be considered undervalued and should be purchased.
If a portfolio provides a return BELOW the SML, it would be considered overvalued and should not be purchased.
SML may be used with individual securities.
Information Ratio
Relative risk-adjusted performance measure
Measures EXCESS RETURN and the CONSISTENCY provided by a fund manager, relative to a benchmark.
The higher the excess return (Information Ratio) the better
Excess return can be positive or negative depending on the fund’s performance relative to its benchmark.
IR = (Rp - Rb) / σA
Rp = portfolio’s actual return
Rb = benchmark return
Rp - Rb = excess return
σA = tracking error of active return (standard deviation of the difference between portfolio returns and index returns)
Treynor Ratio
Tp = (rp - rf) / βp
rp = realized return of the portfolio rf = risk free return βp = beta of the portfolio
Measures risk-adjusted performance of a portfolio manager
Relative risk-adjusted performance indicator, i.e., one Treynor ratio needs to be compared to another to provide meaning
ONLY appropriate when R² > 0.70
Measures how much return was achieved for each unit of risk; higher Treynor ratio means more return was provided for each unit of risk. Measures reward achieved relative to the level of systematic risk (as defined by Beta) - accomplished by standardizing portfolio returns for volatility.
Treynor justifies use of the model on the assumption that in a well-diversified portfolio, unsystematic risk is always close to zero.
Treynor Index does not indicate whether a portfolio manager has outperformed or underperformed the market.
EXAM TIP: Use for well-diversified portfolios because Treynor uses Beta!
Sharpe Ratio
Risk adjusted performance measure that measures reward to total variability or total risk (standard deviation):
Sp = (rp - rf) / σp
rp = realized portfolio return rf = risk free return σp = standard deviation of the portfolio
Relative risk adjusted performance indicator, thus needs to be compared to another Sharpe ratio to provide meaning
ONLY appropriate when R² < 0.70
When R² is low, you need to consider all risks and would use standard deviation as the risk statistic.
Measure of how much return was achieved for each unit of risk; the higher the Sharpe Ratio the better (more return was achieved for each unit of risk).
Measures risk premiums of the portfolio relative to the total amount of risk in the portfolio.
Does NOT measure a portfolio manager’s performance against that of the market.
EXAM TIP: Use for non-diversified portfolios because Sharpe uses Standard Deviation.
Jensen Model or Jensen’s Alpha
Differs from Treynor and Sharpe in that it can distinguish a manager’s performance relative to that of the market and determine differences between realized (actual) returns and required returns as specified by CAPM.
While Treynor and Sharpe provide measure for relative performance, Jensen’s Model measures absolute performance on a risk-adjusted basis.
Positive Alpha → fund manager provided more return than expected for risk taken
Negative Alpha → fund manager provided less return than expected for risk undertaken
Alpha = 0 → fund manager provided return equal to expected return for risk taken
- quantifies risk-adjusted return
αp = rp - [rf + (rm - rf) βp]
rp = realized portfolio return rf = risk-free return rm = expected return on the market βp = beta of portfolio αp = measure of portfolio manager's contribution to the return
The higher the alpha, the better the performance. Negative alphas indicate managers who have underperformed the market on a risk-adjusted basis.
Only when BETA = 1, ALPHA = amount a fund beat the market!
Sharpe, Treynor, and Alpha Application
Both TREYNOR and ALPHA use Beta as measure of risk, thus, Treynor and Alpha are appropriate risk-adjusted performance indicators for a DIVERSIFIED portfolio, i.e., when R squared ≥ 0.70.
When R squared ≤ 0.70, the portfolio is not well diversified, thus Standard Deviation is an appropriate risk-adjusted measurement, thus using SHARPE is appropriate.
EXAM TIP: if exam doesn’t give you R Squared, select Sharpe!
Effective Annual Rate (EAR)
Calculates effective annual interest rate earned on an investment when compounding occurs more often than once a year
EAR= (1 + i/n)^n -1
i = stated annual interest rate n = number of compounding periods
Example: Effective annual rate of 10% compounded quarterly:
(1+ 0.10/4)^4-1 = 10.38%
Arithmetic Average / Simple Average
AM = (a1 + a2 + a3 + an) / n
OR on calculator:
a1 Σ+ a2 Σ+ a3 Σ+ an Σ+, Orange shift x̄, ȳ
ignores compounding effect over time
Geometric Average = Time weighted return
Time weighted compounded rate of return:
GM = n√(1 + r1) * (1 + r2) * (1 + r3) − 1
(May not be appropriate for a time series of asset returns due to possibility of a zero or negative return and due to compounding)
Weighted Average
of a share price:
(Σ (# of shares x price per share)) / total # of shares
of portfolio return or weighted Beta (same calculation):
Σ((%weight A x %return A) + (%weight B x %return B) +(%weight N x %return N))
Net Present Value
Used to evaluate capital projects and capital expenditures that will result in differing cash flows over the useful life or investment period.
The method discounts future cash flows at an appropriate discount rate and allows the present value of the inflows to be compounded to the present value of the outflows.
Discount rate = investor’s required ROR.
NPV = deterministic: if NPV = positive, investor would make the investment (actual return > required return), if negative, investor would not make the investment (actual return < required ROR); if NPV = 0, return meets required return, investor should make investment.
NPV = PV of Cash Flows - Initial Cost
+/- Initial cost = CF0
If sold in last year, add sales price to last year cash flow.
Solve for NPV
Internal Rate of Return (IRR)
IRR allows financial planner to compare computed rate to required ROR
The method discounts future cash flows at an appropriate method used to determine the exact discount rate to equalize cash inflows and cash outflows of a specific investment or project.
IRR = discount rate that sets the NPV formula equal to zero
IRR calculation assumes reinvestment rate = IRR
Accept project where IRR > required ROR
YTM and YTC are examples of IRR calculation.
Can be thought of as a compounded rate of return.
IRR should be calculated when you have uneven cash flows and you are asked to calculate a compounded rate of return.
If NPV is positive, IRR > Discount Rate
If NPV is negative, IRR < Discount Rate
If NPV = 0, IRR = Discount Rate
NPV is considered superior model to IRR when comparing investment projects of unequal lives.
Investing at the required ROR is more reasonable than at the IRR.
With changes of more than 2 inflows or outflows in an investment project there will be only one NPV, however, multiple IRRs.
If NPV and IRR suggest two different investment projects, select the project with the higher positive NPV!
Dollar Weighted Return
Calculates IRR using investor’s cash flows:
Bob purchases 1 share of DIS for $50. One year later the stock pays a $4 dividend, and Bob purchases an additional share for $65. Bob sold the stock one year later for $75/share. What was Bob's dollar weighted return? Period Cash Flow 0 +/- 50 1 +/- 61 2 150 IRR = 22.63%
Holding Period Return with Margin Interest
Bob bought 100 shares of CISCO at $20/share; initial margin was 60%, he was charged 10% margin interest annually. After 1 year he sold the shares at $30/share. What is his HPR?
(3000 - (2000 x 0.6) - (2000 x 0.4 x 0.1) - (2000 x 0.4)) / (2000 x 0.6)
Where:
2000 x 0.6 = initial equity
2000 x 0.4 x 0.1 = margin interest paid
2000 x 0.4 = to be paid back
After Tax Holding Period Return
Bob bought 100 shares of CISCO at $20/share; initial margin was 60%, he was charged 10% margin interest annually. After 1 year he sold the shares at $30/share. Bob is in the 35% tax bracket and his LT capital gains tax rate is 15%. What is his after tax HPR?
(3000 - (2000 x 0.4) - ((2000 x 0.6) x (1 - 0.15)) - ((2000 x 0.4) x (1 - 0.35)) - ) / (2000 x 0.6)
Where: 2000 x 0.6 = initial equity 2000 x 0.4 = to be paid back (2000 x 0.6) x (1 - 0.15) = LTCG tax (2000 x 0.4) x (1 - 0.35) = interest income tax
Arbitrage Pricing Theory
- pricing imbalances cannot exist for a significant period of time, otherwise, investors will exploit the price imbalance until market prices are back to the equilibrium
- attempts to take advantage of pricing imbalances
- multi-factor model that attempts to explain return based on factors
- anytime a factor has a value of zero, that factor has no impact on the return
- inputs are factors, such as inflation, risk premiums, expected returns, and their sensitivity to those factors
- Standard deviation and Beta are NOT input variables to the APT
How do mutual funds report?
Mutual funds report on a time-weighted basis.
Foreign Currency Translation
- Convert US Dollars to foreign currency to determine the cost
- Compute the return, typically using HPR
- Convert foreign currency back to US Dollars
Example:
100 shares in Intl. Easy Co. @ £12.75 when currency rate is $1.50/£ with transaction costs of £25.
Cost in £ = £12.75 x 100 + £25 = £1,300
Cost in $ = £1,300 x $1.50 =$1,950
If stock price increases to £17.50 a share, transaction cost to sell are £25 and currency rate is now$1.55/£, what is the gain in US dollars? 37.12% (HPR) or $723.75
Dividend Discount Model (aka Intrinsic Value Model)
The Constant Growth Dividend Discount Model values a company’s stock by discounting the future stream of cash flows.
V = D1 / (r-g)
r = required ROR g = dividend growth rate D1 = next expected dividend
Calculated using current dividend and dividend growth rate as follows: D1 = D0 (1+g)
Expected Rate of Return
r = (D1 / P) + g P = market price or value
If the required ROR decreases, the stock price increases.
If the dividend is expected to increase, the stock price will increase.
If the required ROR increases, the stock price will decrease.
If the dividend is expected to decrease, the stock price will decrease.
Sample calculation:
current annual dividend = $2/share
5 years ago the dividend was $1.36/share
Dividend is expected to grow at the same compound annual rate as the past 5 years.
Required ROR = 12%
Expected return on the market portfolio = 14%
What is the value of a share of common stock using the constant dividend growth model?
N = 5
PV = +/-1.36
FV = 2
Solve for I/YR: 8.02%
V = D1 / (r-g)
2 (1.0802) / (0.12 - 0.0802) = $54.28
Yield Curve Types
Normal / Upward sloping yield curve: short term rates are lower than long term rates
Flat: short and long term rates are similar
Inverted / Negative sloping: short term rates are higher than long term rates
(An inversion of the yield curve is indicative of a looming recession. Long-term investors will settle for lower yields.)
What is the yield curve a function of?
business cycle - longer end of the curve is a market rate and predicts anticipated economic conditions
Fed policy - short end of the curve is very sensitive to Fed policy (e.g., if fed aggressively increases the discount rate and predictions are keeping the longer end of the curve down, an inverted curve will likely be the result)
Valuation of Bonds takes into consideration……
bond’s coupon payments (PMT) (assume semi-annual compounding: payment per period is half of the coupon)
market rate of interest for comparable bonds (I/YR)
amount of time remaining to maturity (N)
maturity / par value (assuming $1,000) (FV)
(Solve for PV to get the bond’s intrinsic value)
Financial Markets
Provide for exchange of capital and credit in the economy
Money Markets - short term debt instruments
Capital Markets - long term debt and equity instruments; consist of Primary and Secondary Markets
Primary Market
New securities issued and sold to the public for the first time
- registered with the SEC and sold to clients through IPO process
- issuing firm = recipient of proceeds
- Primary Markets and issues = regulated by Securities Act of 1933
Secondary Market
previously issued securities trade among investors
- issuing company not directly involved
- Secondary Markets and issues = regulated by the Securities Act of 1934
- 2 forms of Secondary Markets:
1. Organized Exchange (NYSE)
2. OTC (NASDAQ)
Efficient Market Theory
Stock market = efficient, all stocks reflect relevant information and are priced in equilibrium.
Investors who accept EMT would be passive investors and buy only index funds
Strong Form
Semi Strong Form
Weak Form
EMT - Strong Form
Investor has no access to
Technical Analysis
Fundamental Analysis
Insider Information
EMT - Semi-Strong Form
Investor has
Access to Inside Information
No Access to Fundamental or Technical Analysis
EMT - Weak Form
Investor has
Access to Insider Information and Fundamental Analysis
No Access to Technical Analysis
Market anomalies
Cannot be explained away by EMT
- Low P/E effect
- Small Firm effect
- Neglected Firm effect
- January effect
- Value Line Phenomenon
Time weighted return
global standard for fund performance
based solely on appreciation or depreciation of a portfolio from period to period
Nominal yield of a bond
coupon yield
Current yield
annual coupon / current market price
YTM - YTC- YTW
YTM and YTC are calculated in similar ways. When asked which yield is appropriate to make an investment decision, choose the lower one (= YTW)
What happens to the intrinsic value of an existing bond when the current yields are higher than the coupon rate?
Intrinsic value of the existing bond goes up
What does duration calculate?
time to recoup your money on a bond investment (= effective maturity)
used to estimate changes in bond prices based on hypothetical changes in prevailing rates (a 1% change in rates would lead to roughly a % change in bond’s price equal to duration expressed as a percent)
What is duration?
Weighted average of the Present Values of the future cash flows of a bond / bond portfolio
always stated in years
for income producing bonds, duration will always be shorter than maturity
for Zero Coupon bonds, duration = maturity
Duration increases with maturity
higher coupon → lower duration
Duration = linear estimate, tends to overestimate risks from rising interest rates and underestimate benefits from lowering interest rates
What does matching the duration of a fixed income portfolio to investor’s time horizon do?
It immunizes those assets, thus, significantly reduces purchasing power and reinvestment rate risks for the assets
Estimating Change in Bond Price
Rate Decrease leads to Price Increase
Rate Increase leads to Price Decrease
A 1% change in rates roughly equals a % change in bond’s price that is equal to the duration expressed as a percent.
Short end of the curve will not move too much with rate changes.
Long end of the curve will move significantly with rate changes.
The LONGER the duration and the LOWER the coupon, the MORE SENSITIVE to rate changes.
The SHORTER the duration and the HIGHER the coupon, the LESS SENSITIVE to rate changes.
(If asked to calculate price change in portfolio, multiply percentage change in price by $$ in portfolio.)
To determine the holding period of an asset, the day of acquisition is _______ and the disposal date is ______.
The day of acquisition is excluded
the day of disposal is included
Calculating average (mean) return and Standard Deviation with calculator
returns:
20%, 15%, -9%, 34%, -16%
What percentage of the time would you expect a return between-12% and -32.8%?
20 Σ+ 15 Σ+ 9, +/- Σ+ 34 Σ+ 16, +/- Σ+ Shift, 7 (x,y) - mean Shift, 8 (sx, sy) - SD
Comparing Sharpe, Treynor, and Jensen’s Alpha
Sharpe Treynor Jensen’s Alpha
What? risk adjusted return risk adjusted return excess return
When? R² < 0.70 R² > 0.70 R² > 0.70
Value relative relative absolute
Relevant Standard Beta Beta
Risk Statistic Deviation
Wash Sale
- investors cannot deduct losses from sales or trades of stock or securities in a wash sale unless the loss was incurred in the ordinary course of their business as a dealer in stock or securities
Wash sale: occurs when taxpayer realizes a loss on the sale of a security and acquires a substantially identical security within a 61-day period (30 days prior to the trade date to 30 days after the trade date)
Substantially identical:
- bonds: unless exact same bond or bond fund is purchased, it is difficult to violate the wash sale rule with fixed income
- stocks that trigger “substantially identical”: convertible bond (can convert to same stock that was sold for a loss); purchase a call option that can be exercised into the same stock that was sold for a loss
Wash sale ramifications:
- loss on sold security will be disallowed
- disallowed loss will be added to basis of new securities purchased
- when new (replacement) securities are sold (via higher cost basis), loss will be allowed eventually
Multi-Stage Dividend Discount Model
Example:
Patrick bought 1000 shares of BIF
Current dividend $4.00
Dividends are expected to grow 5% annually for the next 3 years
After 3 years, BIF dividends are projected to grow at 4%
Patrick’s required ROR = 8%
What is the valuation of BIF stock?
Step 1:
D1 = D0 x (1+g) = 4.20
D2 = D1 x (1+g) = 4.41
D3 = D2 x (1+g) = 4.63
Step 2:
(4.63 x 1.04) / (0.08 - 0.04) = 120.38 + 4.63 = 125.01
Step 3: Solve for NPV 8 I/YR 0 CF0 4.2 CF1 4.41 CF2 125.01 CF3 Shift, NPV = 106.91
Stock Option Contracts
Buyer = holder, long Seller = writer, short
Buyer of the contract has the right (or option) to do the following:
- call contract: right to purchase shares
- put contract: right to sell shares
Seller of the contract has the obligation to do the following:
- call contract: obligation to sell shares
- put contract: obligation to buy shares
The buyer of the contract pays the seller a premium to enter the contract.
Premium is $ per share.
Premium presents:
- maximum possible loss for buyer
- maximum possible gain for seller
All contracts will stipulate:
- exercise price - expiration date
All contracts cover 100 of the underlying stock.
Value comes from favorable difference between market price of the stock and the exercise price of the contract,
- know as “in the money”:
- for a call favorable difference is when MP > EP
- for a put favorable difference is when MP < EP
If there is no favorable difference, option is “out of the money”.
If MP = EP, option is “at the money”.
Options Clearing Corporation (OCC) guarantees the performance of both parties.
- eliminates counterparty risk
Both the buyer and the seller of an option can be bullish or bearish on the underlying stock.
Options Strategies
Long Straddle↓ Short Straddle ↓
Buy (hold) Sell (write)
Call Bull ↑ Bear ↓
Spreads
Put Bear ↓ Bull ↑
Spreads
To arrive at the profit net the premium paid from the current gain!
Stock Option Premiums
The premium is the price the option buyer pays to the option seller to establish the option contract.
- premium is paid on a per-share basis
- 2 basic variables and 5 expanded variables that determine an option’s price:
- intrinsic value: market price of underlying stock
exercise price of option contract - Time premium: risk-free rate of return
time to expiration
variability of underlying stock (as measured by standard deviation)
The greater any or all of the 3 expanded variables, the greater the time premium
Time premium is greatest at the creation of the contract and approaches $0 at the expiration of the contract.
Intrinsic value can never be less than $0.
Options Premiums
Option Type Total Premium EP MP Intrinsic Value Time Premium
Call $5 $30 $32 $2 $3
Call $4 $60 $58 $0 $4
Call $8 $20 $25 $5 $3
Put $7 $45 $44 $1 $6
Put $2 $75 $85 $0 $2
Put $6 $90 $92 $0 $6
Intrinsic Value calculations:
Intrinsic Value for Call options: COME: Call Option = Market Value - Exercise Price
Intrinsic Value for Put option: POEM: Put Option = Exercise Price - Market Value
Stock Option Strategies
Used to hedge existing stock position or to speculate on stock without owning it
- Covered call writing: Long the underlying stock - short the call
- Only considered covered if you own enough shares to cover all contracts sold
- Used to generate income for portfolio - Naked call writing: does not own underlying stock - short the call
- unlimited risk for writer - Protective put: Long the stock - long the put
- portfolio insurance - Protective call: Short the stock - long the call
- used to protect a short position in the stock - Covered put: Short the stock - short a put
- writer uses the stock put to cover their short stock position - Collar (Zero cost collar): Long the stock - long the put - short the call
- put is used to protect against a stock price decrease, call premium used to
offset cost of the put - Straddle: Long a put and a call on the same underlying stock with the same
expiration date and strike price
- used to capitalize in volatility regardless of the direction - Spread: involves purchasing and selling same type of contract
- benefit from stability (i.e., minimum moves in underlying stock’s price)
Futures Contracts
Agreement to buy or sell a specific amount of commodity, a currency, or a financial instrument at a particular price on a stipulated future date.
Spot price = current market value of the item in today’s market (e.g., melt value of gold)
Futures contract allows speculation and hedging on the spot price at some point in the future (almost all contracts are settled through an offsetting contract, not through physical delivery)
Futures contracts are standardized
Clearinghouse acts as intermediary that guarantees performance of both parties involved in the contract and eliminates counterparty risk.
Using futures for hedging strategies:
- long position: if you own something you are long (e.g., corn farmer is long corn)
- short position: if you have to buy something, you are short (e.g., construction company that needs to build is short lumber)
- Short hedge: anyone who is long needs a short hedge (selling a futures contract establishes a short hedge)
- Long hedge: anyone who is short needs a long hedge (buying a futures contract establishes a long hedge)
Forward contracts are different in that they are not standardized (can take any form the parties agree to) and are not executed through a clearinghouse, thus cary counterparty risk
Financial Ratios
Sri owns a 6-month T-Bill ($1,000 face value) with a discount rate of 2.75% that matures in 120 days. If he were to sell this T-Bill today, how much would he receive?
$1,000
$990.83
$993.99
$999.98
If Sri’s T-Bill were sold today, he would receive $990.83, calculated as follows:
Face Value × [1 - ((Days to Maturity ÷ 360) X Yield)] = Current Price
$1,000 × [1 – ((120 ÷ 360) × 0.0275)] = $990.83
If a bond’s conversion ratio is 75 shares of stock per bond and the price of the stock is $12.75, would it be beneficial for the bondholder to convert?
Yes
No
Not enough information provided.
Since the conversion price is $1,000/75, or, $13.34 per share, the investor can convert and sell the shares for $12.75. This would create a $0.59 loss per share or a total loss of $44.25 ($0.59 x 75 shares).
Because the conversion would result in a loss, the bondholder should not convert.
When you hold a bond and interest rates decrease below the coupon rate, your bond will be a _____________ bond.
premium
disount
When interest rates decrease below the stated interest of the debt (the coupon rate), the security will be worth more since new debt pays less interest. Therefore, the market price for the debt would be above par value, otherwise known as a premium bond.
Internal rate of return is also referred to as the _____________ return.
IMPLIED
Which of the following are variables used to replace dividends when calculating the intrinsic value of a stock using expected earnings?
Payout Ratio
Expected Earnings
Growth Rate of Earnings
Required Rate of Return
Payout Ratio and Expected Earnings
Dt = (Pt)(Et); dividends are replaced by the payout ratio multiplied by expected earnings. When solving for the normal price/earnings ratio, the expected earnings is divided into the intrinsic value.
Determining the most efficient portfolio
Divide standard deviation by return to determine Coefficient of Variation. This tells us the unit of risk per unit of return. The lowest one is the most efficient portfolio!
Characteristics of a normal yield curve
Short-term yield is lower than long-term yield
A ladder structure will be the most beneficial in a normal upward sloping yield curve indicating higher yield at longer maturities, with a stable interest rate environment.
(Barbells work better in a flat yield curve while bullet works better for a steep yield curve.)
In what interest rate environment is a collar beneficial?
A collar is beneficial when the rate goes above the cap.
What is integrated asset allocation?
Integrated asset allocation considers the investor’s goals and policies and capital market conditions, and then uses these data as inputs to some kind of optimizer. The optimizer’s solution becomes the new inputs that are reconsidered along with the investor’s latest goals and policies and most recent market conditions when revising the asset allocation.
