BU - Formulas Flashcards
Constant Growth Dividend Discount Model (DDM)
Calculates the value of a dividend-paying security (with constant growth) in dollars
Step 1 find D1 = Next year’s dividend (Take this year’s dividend x (1+ dividend growth))
Step 2 apply to formula r = required rate of return g = dividend growth rate The question will ask “What is the intrinsic value of the stock?”
When intrinsic value (IV) < market value…
The stock is overvalued and expected return (Er) < required return (k)
the investor should avoid the stock
When intrinsic value (IV) > market value (MV)….
the stock is undervalued and expected return (Er) > required return (k)
the investor should buy the stock
What does the expected rate of return do?
It is the rate an investor should expect based on the price paid for a security
Step 1 find D1 = Next year’s dividend (Take this year’s dividend x (1+ dividend growth))
Step 2 apply to formula
P = market price paid for a security
g = dividend growth
Covariance
Measures how one security behaves as a direct result of another
ρij = correlation between securities i and j (correlation coefficient) σi = standard deviation of security i σj = standard deviation of security j
What does a positive covariance indicate?
What does a negative covariance indicate?
A positive covariance would indicate that two investments would tend to move in the same direction.
A negative covariance would indicate that two investments would tend to move inversely
Standard Deviation of a Two Asset Portfolio
Provides the weighted standard deviation for a two-stock portfolio
Wi = weight of stock 'i' Wj = weight of stock 'j' σi = standard deviation of stock 'i' σj = standard deviation of stock 'j' COVij = covariance between ‘i’ and ‘j’ - this may not be given, but correlation coefficient will be instead
Will ask “what is the weighted standard deviation of the portfolio?”
Why do you want to know the standard deviation?
to understand how much an investment’s return can vary from the expected return
Expected return on a multiple asset portfolio
Expected return = (weight of investment A x expected return of investment A) + (weight of investment B x expected return of investment B)
What does Beta do?
Provides risk as a measure of volatility relative to that of the market.
helps the investor understand how volatile an investment is relative to a relevant benchmark.
σi = standard deviation of the individual security ρim= correlation between an individual security and the market COVim= covariance between an individual security and the market σm = standard deviation of the market
Market beta is always assumed to be…
1.0
An investment with a beta of around 1.0 will have a similar performance to the market in a given time period.
An investment with a beta of less than 1.0 will be less volatile than the market.
With a beta greater than 1.0, the investment will be more volatile than the market.
Standard Deviation of a Population
Identifies the deviation of a single security over a series of periods of return
σr = standard deviation of results from the expected return Σ = summation of all terms n = number of periods being considered rt = actual return r¯ = average return
Standard Deviation of a Sample
Identifies the deviation of a single security over a series of periods of return -
Don’t have to use formula - calculator can solve with just the return of each period
Sr = standard deviation of results from the expected return Σ = summation of all terms n = number of periods being considered rt = actual return r¯ = average return
Capital Asset Pricing Model (CAPM)
Used to determine a theoretically appropriate required rate of return of an asset.
ri = the investor's required rate of return rf = risk-free rate (T-Bill rate serves this end) rm = return of the market (S&P 500 or some broad index) - may be given **_“market premium”_**, which is (rm-rf) βi = beta of the security being measured for the required return
Question will ask “what will the investor should expect as a return?”
Jensen’s Performance Index (Alpha)
Measures the performance of a portfolio manager relative to the performance of the market
Basically return of the portfolio minus CAPM or Actual Return - Expected Return
αp = difference of return from the amount required by investors rp = return of the portfolio rf = risk-free rate of return rm = return of the market - may be given **_“market premium”_**, which is (rm-rf) βp = Beta of the portfolio being measured
Question will ask “what is the alpha on a portfolio”
If alpha is positive…
If alpha is negative…
If alpha is zero…
+ portfolio manager provided a greater return than was expected given the amount of risk the portfolio was exposed to in terms of beta
- the portfolio manager provided less return than what was expected given the amount of risk the portfolio was exposed to in terms of beta
0 the portfolio manager provided the exact amount of return that was expected given the amount of risk the portfolio was exposed to in terms of beta. This would plot right on that security market line (SML).
Treynor Ratio
Measures the risk adjusted performance of a portfolio manager
Tp = Treynor Index rp = return of the portfolio rf = risk free rate of return βp = beta of the portfolio being measured
Comparing Treynor Ratios: the higher the ratio the greater risk-adjusted rate return
If the R2 is substantially high enough (R2 > .7), use the ___________ Ratio
If the R2 is not substantially high enough (R2 < .7), use the ___________ Ratio
Treynor
Sharpe
Duration
Identifies the length of time the discounted cash flow of a bond remains outstanding
- c* = rate of interest paid on the coupon
- t* = number of periods to maturity
- y* = Yield to Maturity (as a %)
Change of Bond Price
ΔP = the dollar change in price P = price of a bond ΔP/P= % price change of bond (-D) = the duration in terms of years used as a negative value ∆<sub>y</sub> = the % change in interest rates. If they go down this number should be negative 1+y = 1 + yield to maturity
If the result is + then the bond price will increase, if the result is - then the bond price will decrease
Information ratio
Measures return above benchmark divided by standard deviation - using tracing error
RP = return of a portfolio RB = return of a benchmark σA = tracking error of active return
the manager with the highest information ratio provided the highest risk-adjusted rate of return.
Effective Annual Rate
Accounts for intra-year compounding.
i = interest rate n = number of periods
an investment has a stated return that compounds different than annually
Taxable Equivalent Yield
Provides the return that is required on a taxable investment to make it equal to the return on a tax-exempt investment.
- r* = nominal rate of return (tax exempt rate)
- t* = investor’s marginal tax rate (as a decimal)
helps an investor choose between a taxable corporate bond and a tax-free municipal bond.
Arithmetic Mean
Offers the average of a set of numerical values, calculated by adding them together and dividing by the number of terms in the set
- a* = rate of return for given period
- n* = number of periods
Sharpe Ratio
Measures the risk-adjusted performance of a portfolio in terms of standard deviation
Sp = sharpe Index rp = return of the portfolio rf= risk free rate of return σp = standard deviation of the portfolio being measured
choose the investment with the higher Sharpe Ratio as it will provide a greater risk-adjusted rate of return
Unbiased Expectations Theory (unlikely on test)
Implies long-term investors will choose to purchase debt instruments on whether forward interest rates are more or less favorable than current short-term interest rates
- N* = Term to maturity
- 1R1* = Actual current one-year rate today
- E(2r1*) = Expected one-year rate for period 2
- E(Nr1*) = expected one-year rate for years, i = 1 to N
Holding Period Return
Provides the total return received from holding an asset or portfolio of assets over a period of time
- r* = rate of return for given period
- n* = number of periods
Geometric Mean
States the central number in a geometric progression, also calculable as the nth root of a product of n numbers.
- n* = number of periods
- r* = rate of return for given period
Same as HPR plus the step to do the nth root: [(1 + r1)(1 + r2)(1 + r3]1/n – 1
Compare Sharpe, Treynor & Jensen Alpha
Sharpe: risk adjusted return, r2 < .70, relative value, relevant stat is standard deviation
Treynor: risk adjusted return, r2 > .70, relative value, relevant stat is beta
Alpha: excess return, r2 > .70, absolute value, relevant stat is beta
CAPM is used to…
quantify expected return given a market return and beta of the market
quantify the investor’s required rate of return
to plot the security market line (SML)
CML v. SML
CML uses standard deviation and efficient frontier
SML uses Beta and CAPM
