Enter our weekly multiple choice trivia quiz to win (common FRM exam dilemmas)

Nicole Seaman

Director of CFA & FRM Operations
Staff member
Subscriber
Head on over to our Facebook page to enter our Trivia Contest! You will be entered to win a $15 gift card of your choice from Starbucks, Amazon or iTunes (iTunes is US only)!

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
VAR-chart.jpg


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

futures contract.jpg


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
gamma hull.jpg

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
information ratio.jpg

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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David Harper CFA FRM

David Harper CFA FRM
Subscriber
We forgot to mention that this week's trivia questions are each based on a recent thread in the forum that I thought would make an interesting Q&A, so the answers will link to further discussion. :) Thanks!
 

Nicole Seaman

Director of CFA & FRM Operations
Staff member
Subscriber
Today is the last day to get your trivia answers in!! Make sure to get them in for your chance to win!! :)
 

Nicole Seaman

Director of CFA & FRM Operations
Staff member
Subscriber
Thank you to everyone who participated in our trivia contest this week!

The winners are:

@kylevandusen and @mshah6490

Please contact me on the forum or through email at [email protected] to claim your prize. You can choose a $15 gift card from Amazon, iTunes (US only) or Starbucks. You can also claim your prize now or let them accrue if you plan to participate again.
 

Nicole Seaman

Director of CFA & FRM Operations
Staff member
Subscriber
Here are the answers to the trivia questions:

1. D. Yes, V(l) = 1-exp[-V(n)]

Sort of a trick question as lognormal VaR, V(l) = 1 - exp[u - σ*z] and the exponent is already the negative of normal VaR, as V(n) = -u + σ*z
Similarly, we can express normal VaR as a function of a given lognormal VaR:
V(l) = 1 - exp[u - σ*z], so
exp[u - σ*z] = 1 - V(l), and take LN() of both sides:
u - σ*z = LN[1 - V(l)], and multiply by (-1):
-u + σ*z = V(n) = -LN[1 - V(l)]
Inspired by comment at https://forum.bionicturtle.com/thre...st-win-prizes-var-hodgepodge.7688/#post-28849

2. C. It impacts the theoretical price of the futures contract
Discussion at https://forum.bionicturtle.com/threads/l1-t3-148-futures-delivery-process.4401

3: B. The formula returns gamma for a single long option. "Position gamma" multiplies this by quantity and can be negative. As percentage gamma is positive, a short option will have negative position gamma.
For example, a short position in 100 options where each option has percentage gamma of 0.02 has a position gamma of -100 * 0.02 = -2.0
Inspired by discussion at https://forum.bionicturtle.com/threads/hull-11-03.3813

4. D. All of the above (are ratio consistent)
IR is a measure of relative return to risk, as in "relative to a benchmark." There are at least two ways to measure relative return: active or residual (alpha), but the key quality is ratio consistency.
IR = (relative return)/StdDev(same relative return metric); i.e., if alpha is the numerator, then generally we want StdDev(alpha) in the denominator.
Inspired by https://forum.bionicturtle.com/threads/information-ratio.7712/
 
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