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If you do not have Facebook, you can enter right here in our forum. Just answer the following questions:
(Note: All participants will be entered into our random drawing regardless of correct or incorrect answers. There will be two winners drawn at random.)
Question 1
The FRM's most common single-period value at risk (VaR) metric assumes normally distributed arithmetic returns, call this V(n). Given expected return (u) and volatility (sigma) it says: As a percentage of the portfolio's initial value, absolute one-period VaR, V(n,C) = -u + sigma*deviate(C). For example, if drift is +3% and volatility is 10%, then V(n, 95%) = -3% + 10%*1.645 = 20.263%.
Alternatively, lognormal VaR assumes geometric returns such that the future asset price has a lognormal distribution, which precludes a negative future asset price. Call this lognormal VaR, V(l). If we are given a value for V(n), can we convert it to its lognormal equivalent, V(l), where the drift and volatility parameters are the same, but we aren't given these parameters?
a. No, no analytical translation is possible
b. Yes, but the translation includes multivariate integral
c. Yes, V(l) = -LN[1 - V(l)]
d. Yes, V(l) = 1-exp[-V(n)]
Question 2
The FRM appears to distinguish between futures contracts where the underlying commodity is an "investment asset," such as the S&P 500 Index, as opposed to a "consumption asset," such as corn or copper? Given they are all arguably commodities, why distinguish?
a. It's just semantic, both are commodities subject to similar specifications under a standardized contract
b. It speaks to where the contract trades
c. It impacts the theoretical price of the futures contract
d. It identifies the set of commodities which incur a storage cost
Question 3
According to Hull, the gamma of a European call or put option on a non-dividend-paying stock is given by gamma(Γ) = N'(d1)/[S*σ*sqrt(T)]. The numerator is the probability density function (pdf) of the standard normal, which is aways positive; the denominator must always be positive as stock price (S), volatility (σ), and maturity(T) must each be positive. Therefore gamma(Γ) must be positive. However, Hull includes examples with negative gamma; e.g., "Suppose that a portfolio is delta neutral and has a gamma of -3,000 ...." How is it possible that gamma can be negative if the function output must be positive?
a. The formula for gamma contains a typo. When fixed, the gamma function can produce a negative
b. The formula returns gamma for a single long option, which is multiplied by quantity to obtain "position gamma" which can be negative
c. The examples are unrealistic: an actual portfolio would not exhibit negative gamma
d. The formula assumes an INCREASE in the stock price: if the stock price decreases, then then gamma is negative
Question 4
In the FRM, the information ratio (IR) appears to have different definitions. Which of the following is the correct definition of IR?
a. IR = (alpha)/(residual risk)
b. IR = (active return)/(active risk)
c. IR = (relative excess return)/(tracking error), where relative = "relative to benchmark"
d. All of the above
If you do not have Facebook, you can enter right here in our forum. Just answer the following questions:
(Note: All participants will be entered into our random drawing regardless of correct or incorrect answers. There will be two winners drawn at random.)
Question 1
The FRM's most common single-period value at risk (VaR) metric assumes normally distributed arithmetic returns, call this V(n). Given expected return (u) and volatility (sigma) it says: As a percentage of the portfolio's initial value, absolute one-period VaR, V(n,C) = -u + sigma*deviate(C). For example, if drift is +3% and volatility is 10%, then V(n, 95%) = -3% + 10%*1.645 = 20.263%.
Alternatively, lognormal VaR assumes geometric returns such that the future asset price has a lognormal distribution, which precludes a negative future asset price. Call this lognormal VaR, V(l). If we are given a value for V(n), can we convert it to its lognormal equivalent, V(l), where the drift and volatility parameters are the same, but we aren't given these parameters?
a. No, no analytical translation is possible
b. Yes, but the translation includes multivariate integral
c. Yes, V(l) = -LN[1 - V(l)]
d. Yes, V(l) = 1-exp[-V(n)]
Question 2
The FRM appears to distinguish between futures contracts where the underlying commodity is an "investment asset," such as the S&P 500 Index, as opposed to a "consumption asset," such as corn or copper? Given they are all arguably commodities, why distinguish?
a. It's just semantic, both are commodities subject to similar specifications under a standardized contract
b. It speaks to where the contract trades
c. It impacts the theoretical price of the futures contract
d. It identifies the set of commodities which incur a storage cost
Question 3
According to Hull, the gamma of a European call or put option on a non-dividend-paying stock is given by gamma(Γ) = N'(d1)/[S*σ*sqrt(T)]. The numerator is the probability density function (pdf) of the standard normal, which is aways positive; the denominator must always be positive as stock price (S), volatility (σ), and maturity(T) must each be positive. Therefore gamma(Γ) must be positive. However, Hull includes examples with negative gamma; e.g., "Suppose that a portfolio is delta neutral and has a gamma of -3,000 ...." How is it possible that gamma can be negative if the function output must be positive?
a. The formula for gamma contains a typo. When fixed, the gamma function can produce a negative
b. The formula returns gamma for a single long option, which is multiplied by quantity to obtain "position gamma" which can be negative
c. The examples are unrealistic: an actual portfolio would not exhibit negative gamma
d. The formula assumes an INCREASE in the stock price: if the stock price decreases, then then gamma is negative
Question 4
In the FRM, the information ratio (IR) appears to have different definitions. Which of the following is the correct definition of IR?
a. IR = (alpha)/(residual risk)
b. IR = (active return)/(active risk)
c. IR = (relative excess return)/(tracking error), where relative = "relative to benchmark"
d. All of the above
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Thanks!