FFM Exam Study Test with Complete
Solutions 2025
Margin equation - ANSWER margin = equity/ value of security = (value of security -
loan)/value of security
PV, FV, R, T - ANSWER PV = FV/(1+R)^t
Discount factor - ANSWER The value today of a dollar received in the future
Having a higher discount factor means you value money now more than later
Discount factor equation - ANSWER DF = 1/(1+r)^t
Perpetual bonds worth - ANSWER PV = CF/R
Effective annual rate - ANSWER = (1 + (r/n))^n - 1
Expected value equation - ANSWER EV = (P1 * S1) + (P2*S1)+...(Pn*Sn)
Variance - ANSWER σ^2 = E[(Ri(s) - E[RI])^2]
Covariance - ANSWER E[(Ri - E[Ri])(Rj-E[Rj])]
Correlation - ANSWER ρ = cov(Ri, Rj)/σiσj
Risk free asset assumptions - ANSWER E[Rf] = Rf
, V[Rf] = 0
Cov[Rf, Ri] = 0
Expected return of portfolio with Rf and Ri - ANSWER E[Rp] = Rf + wE[Ri-Rf]
Risk premium definition and equation - ANSWER expected value of excess return
E[Ri-Rf]
Excess return - ANSWER Ri-Rf
Portfolio variance - ANSWER w^2σi^2
w^2V[Ri] + (1-w)^2V[Rf] + 2w(1-w)Cov[Ri, Rf]
Sharpe ratio - ANSWER larger = better
(Risk premium)/(risk) = (E[Ri-Rf])/σi
slope of capital allocation line
Mean-variance utility - ANSWER how much doing something makes someone happier
E[Rp] - .5AV[Rp]
here A is risk aversion
Efficient portfolio - ANSWER a portfolio that offers the highest return for its level of risk,
always on capital allocation line
Efficient frontier - ANSWER the combination of all efficient portfolios
Solutions 2025
Margin equation - ANSWER margin = equity/ value of security = (value of security -
loan)/value of security
PV, FV, R, T - ANSWER PV = FV/(1+R)^t
Discount factor - ANSWER The value today of a dollar received in the future
Having a higher discount factor means you value money now more than later
Discount factor equation - ANSWER DF = 1/(1+r)^t
Perpetual bonds worth - ANSWER PV = CF/R
Effective annual rate - ANSWER = (1 + (r/n))^n - 1
Expected value equation - ANSWER EV = (P1 * S1) + (P2*S1)+...(Pn*Sn)
Variance - ANSWER σ^2 = E[(Ri(s) - E[RI])^2]
Covariance - ANSWER E[(Ri - E[Ri])(Rj-E[Rj])]
Correlation - ANSWER ρ = cov(Ri, Rj)/σiσj
Risk free asset assumptions - ANSWER E[Rf] = Rf
, V[Rf] = 0
Cov[Rf, Ri] = 0
Expected return of portfolio with Rf and Ri - ANSWER E[Rp] = Rf + wE[Ri-Rf]
Risk premium definition and equation - ANSWER expected value of excess return
E[Ri-Rf]
Excess return - ANSWER Ri-Rf
Portfolio variance - ANSWER w^2σi^2
w^2V[Ri] + (1-w)^2V[Rf] + 2w(1-w)Cov[Ri, Rf]
Sharpe ratio - ANSWER larger = better
(Risk premium)/(risk) = (E[Ri-Rf])/σi
slope of capital allocation line
Mean-variance utility - ANSWER how much doing something makes someone happier
E[Rp] - .5AV[Rp]
here A is risk aversion
Efficient portfolio - ANSWER a portfolio that offers the highest return for its level of risk,
always on capital allocation line
Efficient frontier - ANSWER the combination of all efficient portfolios
