Investment Flashcards
Stages of Financing
Seed: reasearch and development
First-Stage: initial manufacturing and sales
Bridge: companies that expect to go public w/in a year
Start-Up: product development and marketing for companies that have not publically sold products/services
Alpha
Formula:
Portfolio ROR+[Risk Free ROR-(Market ROR-Risk Free ROR)xBeta]
note: ROR entered as whole numbers NOT decimals
Treynor Ratio
- measure of relative systematic risk using Beta
- Higher T ratio = outperformance
Formula:
- (portfolio ROR - risk free ROR) ÷ Beta
Note: market beta = 1
ROR enterest as decimal along with beta
Beta (β)
- Relative measure of systematic risk
- meaningful if R-squared > .7 (1 = exact)
Investment Beta Formula:
COV btwn asset and market ÷ (SD market) squared
or
(R btwn asset and market x SD asset) ÷ SD market
Portfolio Beta Formula:
Step 1:
FMV A x Beta A = Product A
FMV B x Beta B = Product B
FMV C x Beta C = Product C
Step 2:
(Products: A + B + C) ÷ (FMVs: A + B + C) = Portolio Beta
Efficient Market Hypothesis
Weak:
- assumes market prices incorporate all historical price info
- Technical analysis = useless
- Fundamental analyses = may help
Semi-Strong
- Technical AND Fundamental analysis = useless
- insider info may help
Strong
- Technical, Fundamental AND insider info useless
- throw a dart to decide
Coefficient of Variation
- relative measure of total risk (with standard deviation) per unit of expected return
- compares investments of differing ROR and SD
Formula:
- CV = standard deviation ÷ expected ROR
Lower = better (ie. less risk per unit return)
Options
Call: right to buy @ set price &
- Buy (bull): participate in upward movement ie. “call it in” (gain = unlimited; loss = premium paid)
- Sell/write (bear): expect price to fall (gain = premium received; loss = unlimited if naked)
- buy the right to buy; sell the obligation to sell
Put: Right to sell @ set price
- Buy (bear): downside protection for long position (gain = exercise price - premium paid; loss = premium paid)
- Sell/write (bull): “sell put, buy stock”; expect price to rise (gain = premium received; loss = exercise price - premium received)
- buy the right to sell; sell the obligation to buy
Covered: own security
Naked: don’t own security
Strategies:
- Zero-cost collar: protect gain in long stock position; long stock + long put + short call; cashless -> call premium covers put purchase price
- Straddle: put + call with same price/expiration; long = best if price change > premium paid; short = best if no price change
Think through: did I write or buy? do I owe or receive
Call Up, Put Down
Correlation Coefficient (R) / Coefficient of Determination (r2)
Correlation coefficient ( R or ρ ):
- extent to which two securities are related
- R < +1 –> reduced risk
- can use to reduce risk and increase return for blended portfolios (diversification)
- R = COV ÷ (SD asset 1 x SD asset 2)
Coefficient of determination (R-squared):
- relationship between both variables
- percent variability of asset explained by changes in the market
Standard Deviation (σ)
Measures of variability btwn return and mean
-1x SD = 68%
-2x SD = 95%
-3x SD = 99%
Formula (keystrokes):
1. 2nd, 7
2. (in “X01”) variable 1, enter, down arrow (past Y01 to X02)
3. follow step 2 until all variables entered then…
4. 2nd, 8 (“STAT” screen)
5. 2nd, enter
6. continue step 5 until “1-V” apprears
7. down arrow until “Sx” –> this is SD for data set
example
mean return for Meyer, Inc., is 18% and the standard deviation is 6%. What is the probability of a negative return for Meyer, Inc.?.
1. Zero is 3 standard deviations from the mean [(18% – 0%) ÷ 6%]. The return on Meyer, Inc., should fall within 3 standard deviations of the mean 99% of the time. Therefore, 1% (100% – 99%) of outcomes will fall either below 0% or above 36%.
2. To determine the likelihood that the return will be negative, simply divide the 1% in half. Thus, there is a 0.5% chance that an investor will realize a negative return with Meyer, Inc., stock
Covariance (COV)
- Measures the extent to which two variables (the returns on investment assets) move together
- Needed to calculate Correlation Coefficient
Formula:
COV (btwn 2 assets) = ρ (correlation coefficient btwn assets 1 and 2) x σ (SD) asset 1 x σ (SD) asset 2
Systematic Risk (PRIME)
Purchasing power
Reinvestment rate
Interest rate
Market
Exchange rate
Kurtosis
Leptokurtic
- more peaked
- investors that want to minimize volatility
- “Lept high for Less volatility”
Platykurtic
- less peaked
Z-Score
- Measures the number of SDs a value is from the mean (above or below)
- value > mean = positive and vice versa (ie. z-score of 1.5 = value is 1.5 SD above mean)
Formula
- (value - mean) ÷ SD
Standard Deviation of Two Asset Portfolio
To calculate:
- on formula sheet “W” is the weighting of each asset in the portfolio
- W asset 1 + W asset 2 should be 100%
- COV is R btwn a1 and a2
Holding Period Return
(end value - begin value + CF) ÷ begin value
Arithmetic Mean & Geometric Mean
Arithmetic Mean:
- Same calculation as SD, but look for the X with line over it
- approx earnings rate over time (large YOY fluctuations cause misleading results)
- does not account for reinvestment or compouding
Geometric Mean:
- accounts for compounding
- will always be < arithmetic mean
- To calculate:
PV = -1
FV = (1+ROR1)(1+ROR2)….
N = # years
I/Y = SOLVE
Expected ROR
- Requires Outcomes (ROR %) and Probability
- (Outcome 1 x Probability 1) + (Outcome 2 x Probability 2)…
OR use SML (for expected return of security or investment)
- risk free ROR + (market ROR - risk free ROR) x Beta
Effective Annual Rate (EAR)
low priority…i think
- APR taking compouding into consideration
- provides annual rate if compounding is > 1x per year
EAR = [1 + (interest rate ÷ # periods)] to the power # periods
Time-Weighted & Dollar-Weighted
Time-Weighted
- geometric annual ROR based on current FMV of asset
- preferred for portfolio managers (ie. fund ROR)
- cash flows may distort actual ROR
Dollar-Weighted
- compouded annual ROR (IRR) that discounts portfolio FV and CF to a PV
- assessment of actual performance, including deposits, withdrawals (vs. a manager)
Risk-Adjusted ROR
- use against appropriate benchmark
- best using after-tax ROR (ie. 1-tax rate)
- = actual return ÷ beta
- Methods include:
- Treynor, Sharpe, Jensen
Modern Portfolio Theory
- risk and return = basis for determining efficient portfolios
Efficient Frontier:
- portfolios of EF have highest ROR for given risk
- portfolios can exist below EF, but will be less efficient
- portfolios cannot exist above EF - it is unattainable
Indifference Curves:
- curve upward; each investor has infinite number of ICs
- use with EF to determine optimal portfolio for a given level of risk
- portfolio tangent to EF and IC is optimal for that investor
Capital Asset Pricing Model
- asset expected return = risk free rate + (market rate - risk free rate) x investment beta
market rate - risk free rate = market risk premium
(market rate - risk free rate) x investment beta = investment risk premium - compare w/ investor required return to determine if should buy/sell
Capital Market Line (like EF for CAPM)
- portfolio investment expected return = risk free rate + SD portfolio x (market risk premium ÷ SD market)
- if lending –> left of tangent
- if borrowing –> right of tangent
Securities Market Line:
- same formula as CAPM, but use Beta (not SD)
Bond Valuation
CY = coupon pmts ÷ current price
YTM/YTM = TVM calc (note assumes reinvestment at current rate)
- PV = current value
- FV = maturity value/call value
- PMT = semiannual coupon pmt
- N = years remaining (x 2) to maturity/call
- I/Y = SOLVE ÷ 2 (semiannual pmts)
Bond Valuation Triggers
ADD SOME OF THE MAIN CONCEPTS
Unbiased Expectations Theory
- LT rates consist of many ST rates, so LT rate is Geometric mean of ST rates
- can explain up or down slope tield curves
Yield Curve on Investment Decisions
1) flat = investors should only buy LT bonds if confident LT rates will fall
2) inverted = investors should favor LT maturities, bc curve will correct and ST rates will fall
3) steep slope = investors should avoid LT
Duration & Convexity
Duraiton
- - weighted-avg number of year until investment is recovered
- same duration = same interest rate exposure
- zero-coupon bond duration = maturity (increased cash flow = decreased duration)
- inverse relationship w/ YTM
Convexity
- degree duration changes due to TYM
- generally greatest with 1) low coupon, 2) long maturity, 3) low TYM
Relationship w/ Duration and Convexity:
- coupon = invesrse
- time to maturiy = direct
- YTM = inverse
Duration Calc/Example
ADD
Constant Growth Dividend Discount Model
- best for mature, well established companies
- V = D1 ÷ (required return - div. growth rate)
- if “current” divident provided, increase by growth rate for calc
