Quick Sheet Flashcards
Implementation shortfall
= (execution cost + opportunity cost + fees)/ (total shares in order x decision price)
= paper return - actual return
execution cost = actual sale profit - (shares traded x decision price)
OR = delay costs + trading costs
Execution Cost
= actual sale profit - (shares traded x decision price)
OR
= delay costs + trading costs
Opportunity Cost
= shares remaining unexecuted x (closing price - decision price)
Trading Cost
= actual cost of trade (found sum of all qty x price) - (shares traded x arrival price)
—> arrival and benchmark can be interchanged if specified - assume benchmark is the arrival price
—> trading cost is typically noted in dollars vs arrival cost in bps. If they ask for bps, you divide by the arrival cost
Delay Cost
= (decision price - arrival price) x actual shares traded
Market Adjusted Cost
= arrival cost - (beta x index cost)
–> negative number would indicate a savings
Arrival Cost
= side x [(avg px - arrival price)/ arrival price]
—> arrival cost is noted in bps vs trading cost is dollars
index cost
= side x [(index VWAP - index arrival price)/ arrival price]
Sharpe Ratio
= (asset return - risk free rate) / std. deviation
OR (avg return - min acceptable return) / s.d.
standard deviation
= (asset return - rf rate) / sharpe ratio
OR square root of the variance
Sortino Ratio
= (asset return - risk free rate) / s.d. of negative returns
Target Semideviation
= (asset return - rf rate)/ sortino ratio
Beta
= Covariance/variance
** note that Beta references variance of the BROAD MARKET - if given the s.d. of a sector, note that this is not the s.d. to be plugged into the formula. The s.d. of the market portfolio should be used to calculate variance.
Active Return
= info coef x square root of breadth x s.d. of active return x transfer coef
- info coef: The information coefficient shows how closely the analyst’s financial forecasts match actual financial results. The IC can range from 1.0 to -1.0, with -1 indicating the analyst’s forecasts bear no relation to the actual results, and 1 indicating that the analyst’s forecasts perfectly matched actual results.
- Breadth: The number of truly independent decisions made each year.
- -> if a manager selects ten stocks every month, his breadth is 10 x 12 = 120. If a manager makes a selection every quarter, his breadth is 4
- s.d. of active return: the difference between the benchmark and the actual return aka the active risk
- transfer coef: defined as the correlation between the risk-adjusted alphas and active weights. The TC is an objective measure of how much of the alphas’ information is transferred into a portfolio and is a measure of portfolio construction efficiency
Active Risk
= square root of [ (sum of all :port returns - benchmark returns)^2) / (n-1) ]
–> n = number of return periods
Active Share
= .5 x (sum of all absolute value of weight of security in portfolio - weight in benchmark)
Macaulay Duration
= modified duration x [ 1 + (yield/annual frequency)
Macaulay duration calculates the weighted average time before a bondholder would receive the bond’s cash flows vs modified duration is the price sensitivity to a change in rates
Modified Duration
= macaulay duration / [ 1 + (yield/frequency)
-> change of 20bp increase = -ModDur x .0020
modified duration measures the price sensitivity of a bond when there is a change in the yield to maturity.
–> change in a bonds value given x% interest rate change
Effective Convexity
= [ (P-) + (P+) - (2xPo) ] / ΔCurve^2 x Po)
A second-order effect that describes how a bond’s interest rate sensitivity changes with changes in yield. Effective convexity is used when the bond has cash flows that change when yields change (as in the case of callable bonds or mortgage-backed securities). Similarly, we use the effective convexity to measure the change in price resulting from a change in the benchmark yield curve for securities with uncertain cash flows.
Money Duration vs BPV
money duration = market value x modified duration
BPV = market value x modified duration x .0001
Human Capital
= [ wages x (1+g) x (probability of survival) ] / [ (1+rf rate & any other premiums)^n ]
–> you have to discount each year individually if you are asked to calculate over a span of x years (i.e. 3 years: year one would be discounted at 1.01^1 year 2 1.01^2 year 3 1.01^3 etc)
Core Capital needs
= [ spending x (1+g) x (probability of survival in mortality table) ] / [ (1+rf rate & any other premiums)^n ]
Grinold Kroner Model
= div yield - change in shares outstanding + nominal earnings growth + % change in P/E multiplier
- -> expected income return = dividend yield - change in shares outstanding
- *make sure to consider whether shares are being reduced - i.e. if reducing by 1% you would add dividend yield + 1%
- -> Earnings growth rate = expected inflation + expected real total corporate earnings growth rate
- -> %ΔP/E Multiplier = expected repricing return
- -> dividend yield = dividend / price
Expected income return
= div yield - change in shares outstanding