Formulas

Question 1

CME - GDP Trend Growth

Answer 1

= Labor Inputs + Labor Productivity
= [Growth in potential labor force size + growth in labor force participation] + [growth in capital inputs + growth in TFP]

Question 2

CME: Long-Run Equity Valuation

Answer 2

= (Nominal GDP trend growth) x (Share of profits: dividend rate) x (delta P/E ratio)

Question 3

Taylor Rule

Answer 3

(ioptimal - infl expected) = Realneutral + 0.5(GDPgrowth expected - GDPgrowth trend) + 0.5(Infl expected - Infl target)

Question 4

Grinold-Kroner

Answer 4

E(Re) = GDP growth + LT Corp growth premium + Share repurchase + Div yield + PE growth

Infinite time horizon = GDP Growth + Div Yield

Question 5

Singer Terharr

Answer 5

E(Ri) = Rf + DI(p(i,GM)sdiSR(GM)) + (1-DI)(1sdiSRs)

Question 6

Real Estate Returns

Answer 6

Long-run: E(Rre) = cap rate + NOI Growth Rate

Short-run: E(Rre) = cap rate + NOI Growth Rate - PCT chng in Cap Rate

Question 7

Risky Asset Utility & Weight

Answer 7

U = w^(1-lambda)/1-lambda
Weight = (1/lambda)(mean - rf)/variance

Question 8

Risk budgeting

Answer 8

MCTR = beta(i|p)var(p), ACTR = weight(i)MCTR(i)

Ratio of excess return to MCTR should be same for all assets for AA to be optimal

Question 9

Futures gain/loss

Answer 9

principal invoice amount - bond purchase price

principal invoice amount = (futures settlement price/100)conv factor100,000

Question 10

Beta change using # futures

Answer 10

futures = (Bt - Bs/Bf)*(S/F)

Question 11

Variance Swaps

Answer 11

Strike quoted as s.d.
VarNotional = Vega Notional/2strike
Settlement Amount = (VarNotional)(Realized Var - Var Strike)
Value of swap = VarNotionalPvt(T)[(t/T)(Realized vol(o,t)) + (T-t/T)(Implied vol(t,T)) - Strike^2)

Question 12

Annualizing Volatility

Answer 12

Vol(Monthly) = Vol(Annual)*sqrt(252/21)

Question 13

Fed Funds Rate

Answer 13

Fed Funds Futures Contract Price = 100 - Expected FFR

Prob of change = (futures rate - current)/(FFR with change - current)

Question 14

Min cost HR

Answer 14

h = corr(Rdc,Rfx)*sd(Rdc)/sd(Rfx)

Question 15

Return on leveraged portfolio

Answer 15

ROI*(Ve + Vb) - rb(Vb) / (Ve)

Question 16

Convexity

Answer 16

(MacD^2 + MacD + Disperson)/(1+CFYield)^2

Question 17

BUMs problem

Answer 17

Value-weighted indices have higher allocation to bad bonds with more outstanding debt.

Question 18

Manager Expected Return

Answer 18

IC * Sqrt(BR) * Sd(Ra) * TC

Question 19

Active Share

Answer 19

0.5 * sum over i of abs[Weight(portfolio,i) - weight(BM,i)]

Question 20

Total portfolio variance

Answer 20

sum over i, j of xixjcovi,j

Question 21

Skewness/Kurtosis on downside risk

Answer 21

Positive skewness -> smaller downside risk potential
Excess kurtosis (param > 3) -> greater downside risk potential

Question 22

Deferred CG Tax

Answer 22

FVIF(CG) = (1+r)^n * (1-tCG) + tCG*(Cost/MV)

Question 23

Blended tax environment

Answer 23

Effective return: r* = r(1 - piti - pdtd - pcgtcg)
Effective CG Tax Rate: t* = tcg([1-pi-pd-pcg]/[1-piti-pdtd-pcgtcg]
FVIF(Taxable) = (1+r)^n * (1-T) + T -(1-B)Tcg

Question 24

Equity Duration

Answer 24

De = (A/E)*Da - (A/E-1)(DL)(chng i/chng y)

Question 25

Variance of Equity Duration

Answer 25

= (A/E)2(SigmaA)^2 + (A/E-1)^2(SigmaL)^2 -2(A/E)(A/E-1)(p)(sigmaA)(SigmaL)

Question 26

Brinson-Fachler

Answer 26

Allocation = (wi-Wi)(Bi-B)

Selection & Interaction = Wi(Ri-Bi) + (wi-Wi)(Ri-Bi)