SOA IFM EXAM QUESTIONS AND
CORRECT ANSWERS
Risk Measures (Chp. 2) ANSW✅✅1) Variance (no coherent characteristics)
2) Semi-Variance (no coherent characteristics)
3) VaR (does not satisfy subadditivity unless normal)
4) TVaR (always coherent)
Sensitivity Analysis (Chp. 2) ANSW✅✅Calculating the change in the NPV resulting from a change
in ONE variable at a time.
Designed to identify the variables that are most influential on the success or failure of a project.
Coherent Risk Measures ANSW✅✅1) Translation Invariance
g(x+c) = g(x) + c
Adding a positive amount to a risk adds an equivalent amount to the risk measure.
2) Positive Homogeneity
g(cx) = (c)g(x)
Multiplying a positive amount to a risk will adjust the risk measure in a proportional manner.
3) Subadditivity
g(x+y) ≤ g(x) + g(y) [Upside]
g(x+y) ≥ g(x) + g(y) [Downside]
It is not possible to reduce the capital required to manage a risk by splitting it into separate parts.
There are diversification benefits from combining risks as long as the two risks are not perfectly
correlated.
Purpose of Derivatives (Chp. 1) ANSW✅✅1) Risk Management
2) Speculation
3) Reduced Transaction Costs
4) Regulatory Arbitrage/minimize taxes
,Hedging (Chp. 1) ANSW✅✅Guaranteeing a buying or selling price.
Short Selling Purposes (Chp. 1) ANSW✅✅1) Speculation
2) Financing
3) Hedging
Break - Even Analysis (Chp. 2) ANSW✅✅Determine the value of each assumption parameter so
that the NPV is 0.
4) Monotonicity
g(x) ≤ g(y) if Pr(x ≤ y) = 1 [Upside]
g(x) ≥ g(y) if Pr(x ≥ y) = 1 [Downside]
If one risk always exceeds another, the corresponding risk measures must be similarly ordered.
Scenario Analysis (Chp. 2) ANSW✅✅Calculate the NPV by changing several variables at a time.
Scenario analysis accounts for the fact that variables are interrelated.
Capital Asset Pricing Model Assumptions [CAPM] (Chp. 6) ANSW✅✅1) Buy and sell at competitive
market prices. No taxes or transactions costs. Can borrow and lend at risk free rate
2) hold only efficient portfolios of traded securities
3) Homogeneous Expectations regarding volatility, correlations, and expected returns
MARKET PORTFOLIO == EFFICIENT PORTFOLIO
Capital Market Line (Chp. 6) ANSW✅✅E[Rxm] = rf + [(E[Rm] - rf)/ (σm)] * σxm
The line on the volatility/return graph.
Semi-Variance [Downside Semi-Variance] [Formula] (Chp. 2) ANSW✅✅σ² = E[min(0,(R - µ))²]
Cost of Capital [Formula] (Chp. 7) ANSW✅✅rƒ + β(E[Rmkt]-rƒ)
re = ru + (D/E) (ru-rd)
, Value-At-Risk [VaR] [Formula] (Chp. 2) ANSW✅✅VaRα(X) = Fx⁻¹(α)
Debt Cost of Capital [Formula] (Chp. 7) ANSW✅✅rd = rƒ + β_d(E[Rmkt]-rƒ)
rd = y-pL = yield to maturity - default% * E(loss rate)
Downside Tail Value-At-Risk [TVaR] [Formula] (Chp. 2) ANSW✅✅TVaRα(X) = E[x|x<VaRα(X)] =
(∫xf(x)dx)/α
Levered and unLevered Beta [Formula] (Chp. 7) ANSW✅✅βu = Weβe + Wdβd
βe = βu + (D/E) [βu-βd]
Upside Tail Value-At-Risk [TVaR] [Formula] (Chp. 2) ANSW✅✅TVaRα(X) = E[x|x>VaRα(X)] =
(∫xf(x)dx)/(1-α)
CAPM Holds Unless (Chp. 8)
Mkt port is inefficient ANSW✅✅1) Investors are not rational or are misinformed.
2) Investors hold inefficient investments.
Behavior Biases that do NOT impact market efficiency ANSW✅✅1) Portfolios are not Diversified
a) Familiarity Bias
b) Relative Wealth Concerns
2) Portfolios are Excessively Traded
a) Overconfidence
b) Sensation Seeking
Effective Markets Hypothesis [EMH] (Chp. 4) ANSW✅✅It is difficult or impossible to beat the
stock market.
Behavior Biases that impact market efficiency (SYSTEMATIC) ANSW✅✅1) Disposition Effect--
holding onto losers
CORRECT ANSWERS
Risk Measures (Chp. 2) ANSW✅✅1) Variance (no coherent characteristics)
2) Semi-Variance (no coherent characteristics)
3) VaR (does not satisfy subadditivity unless normal)
4) TVaR (always coherent)
Sensitivity Analysis (Chp. 2) ANSW✅✅Calculating the change in the NPV resulting from a change
in ONE variable at a time.
Designed to identify the variables that are most influential on the success or failure of a project.
Coherent Risk Measures ANSW✅✅1) Translation Invariance
g(x+c) = g(x) + c
Adding a positive amount to a risk adds an equivalent amount to the risk measure.
2) Positive Homogeneity
g(cx) = (c)g(x)
Multiplying a positive amount to a risk will adjust the risk measure in a proportional manner.
3) Subadditivity
g(x+y) ≤ g(x) + g(y) [Upside]
g(x+y) ≥ g(x) + g(y) [Downside]
It is not possible to reduce the capital required to manage a risk by splitting it into separate parts.
There are diversification benefits from combining risks as long as the two risks are not perfectly
correlated.
Purpose of Derivatives (Chp. 1) ANSW✅✅1) Risk Management
2) Speculation
3) Reduced Transaction Costs
4) Regulatory Arbitrage/minimize taxes
,Hedging (Chp. 1) ANSW✅✅Guaranteeing a buying or selling price.
Short Selling Purposes (Chp. 1) ANSW✅✅1) Speculation
2) Financing
3) Hedging
Break - Even Analysis (Chp. 2) ANSW✅✅Determine the value of each assumption parameter so
that the NPV is 0.
4) Monotonicity
g(x) ≤ g(y) if Pr(x ≤ y) = 1 [Upside]
g(x) ≥ g(y) if Pr(x ≥ y) = 1 [Downside]
If one risk always exceeds another, the corresponding risk measures must be similarly ordered.
Scenario Analysis (Chp. 2) ANSW✅✅Calculate the NPV by changing several variables at a time.
Scenario analysis accounts for the fact that variables are interrelated.
Capital Asset Pricing Model Assumptions [CAPM] (Chp. 6) ANSW✅✅1) Buy and sell at competitive
market prices. No taxes or transactions costs. Can borrow and lend at risk free rate
2) hold only efficient portfolios of traded securities
3) Homogeneous Expectations regarding volatility, correlations, and expected returns
MARKET PORTFOLIO == EFFICIENT PORTFOLIO
Capital Market Line (Chp. 6) ANSW✅✅E[Rxm] = rf + [(E[Rm] - rf)/ (σm)] * σxm
The line on the volatility/return graph.
Semi-Variance [Downside Semi-Variance] [Formula] (Chp. 2) ANSW✅✅σ² = E[min(0,(R - µ))²]
Cost of Capital [Formula] (Chp. 7) ANSW✅✅rƒ + β(E[Rmkt]-rƒ)
re = ru + (D/E) (ru-rd)
, Value-At-Risk [VaR] [Formula] (Chp. 2) ANSW✅✅VaRα(X) = Fx⁻¹(α)
Debt Cost of Capital [Formula] (Chp. 7) ANSW✅✅rd = rƒ + β_d(E[Rmkt]-rƒ)
rd = y-pL = yield to maturity - default% * E(loss rate)
Downside Tail Value-At-Risk [TVaR] [Formula] (Chp. 2) ANSW✅✅TVaRα(X) = E[x|x<VaRα(X)] =
(∫xf(x)dx)/α
Levered and unLevered Beta [Formula] (Chp. 7) ANSW✅✅βu = Weβe + Wdβd
βe = βu + (D/E) [βu-βd]
Upside Tail Value-At-Risk [TVaR] [Formula] (Chp. 2) ANSW✅✅TVaRα(X) = E[x|x>VaRα(X)] =
(∫xf(x)dx)/(1-α)
CAPM Holds Unless (Chp. 8)
Mkt port is inefficient ANSW✅✅1) Investors are not rational or are misinformed.
2) Investors hold inefficient investments.
Behavior Biases that do NOT impact market efficiency ANSW✅✅1) Portfolios are not Diversified
a) Familiarity Bias
b) Relative Wealth Concerns
2) Portfolios are Excessively Traded
a) Overconfidence
b) Sensation Seeking
Effective Markets Hypothesis [EMH] (Chp. 4) ANSW✅✅It is difficult or impossible to beat the
stock market.
Behavior Biases that impact market efficiency (SYSTEMATIC) ANSW✅✅1) Disposition Effect--
holding onto losers
