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Question 1 : A long bond position is hedged using a short position in the futures market. If the hedge performs as expected, then which of the following statements is most accurate: (a) the investor will be able to avoid losses but will also forgo the gains on his positions (b) the investor will be able to avoid losses (c) the investor will be able to avoid losses and will also be able to keep the gains on his positions (d) None of the above
The correct answer is choice 'a'
If the hedge performs as expected, then any P&L on the long bond position will be offset by identical losses (or gains) on the hedge. Since hedges are never perfect, and some residual risk such as basis risk, the inability to enter into an unrounded number of futures contracts will remain. However, the bulk of the risk would be mitigated, and the investor will be able to avoid any losses but will also forgo any gains. Therefore choice b is the correct answer and the rest are incorrect.
Question 2 : A risk management function is best organized as: (a) a part of the trading desks and other risk taking teams (b) reporting directly to the traders, as to be closest to the point at which risks are being taken (c) report independently of the risk taking functions (d) integrated with the risk taking functions as risk management should be a pervasive activity carried out at all levels of the organization.
The correct answer is choice 'c'
The point that this question is trying to emphasize is the independence of the risk management function. The risk function should be segregated from the risk taking functions as to maintain independence and objectivity. Choice 'a', Choice 'b' and Choice 'd' run contrary to this requirement of independence, and are therefore not correct. The risk function should report directly to senior levels, for example directly to the audit committee, and not be a part of the risk taking functions.
Question 3 : Which of the following attributes of an investment are affected by changes in leverage: (a) Sharpe ratio (b) Information ratio (c) risk and return (d) All of the above
The correct answer is choice 'c'
Changing leverage does not affect the Sharpe ratio or the Information ratio. However, leverage magnifies both risk and return. Therefore a is the correct answer. Recall that Sharpe ratio is the ratio of the excess returns (over the risk free rate) of an investment to its standard deviation, and the information ratio is the ratio of the 'alpha' returns to the standard deviation of such returns.
Question 4 : For an investor with a long position in market index futures, which of the following is a primary risk: (a) Movement in interest rates underlying the futures prices (b) Increase or decrease in the level of the underlying index (c) Basis risk between futures and spot prices (d) Risk that expected dividends will differ from realized dividend yields
The correct answer is choice 'b'
This question emphasizes the difference between primary and secondary risks. Primary risks are the risks consciously undertaken, ie the risks whose premium the investor is trying to earn. Secondary risks are risks that accompany the primary risks that the investor will either hedge, or will ignore if they are small. It is important to watch out for secondary risks because they could become significant and offset the returns being sought even if the investor's market view is proved correct. An investor in market index futures is betting that the index will rise. Index futures prices are largely driven by the spot value of the index, but are also affected by costs of carry. In particular, futures prices will be driven by interest rates, expected dividends, and any other factors that may cause the basis between spot and futures prices to diverge. These risks are secondary risks. In this question, Choice 'b' represents the primary risk, and Choice 'c', Choice 'a' and Choice 'd' are all secondary risks. Therefore Choice 'b' is the correct answer.
Question 5 : The diversification effect is responsible for: (a) the sub-additivity property of market risk VaR assessments (b) the super-additivity property of market risk VaR assessments (c) VaR being applicable only to short term horizons (d) total VaR numbers being greater than the sum of the individual VaRs for underlying portfolios
The correct answer is choice 'a'
Any good risk measure has the property that it is sub-additive, which means the whole is less than the sum of the parts. In the case of VaR, sub-additivity arises due to the diversification effect, or said differently, due to the correlation between different assets being less than one. Therefore Choice 'a' is the correct answer. Super-additivity is just the opposite of sub-additivity, ie, the whole is greater than the sum of the parts. Good risk measures do not have super-additivity. Therefore Choice 'b' is incorrect.
studies because they no longer exist. Survivorship bias results in past results looking better than they actually were as data points relating to failures are not included. A risk manager needs to be aware of survivorship bias when basing risk analysis on historical data and should question if failures (eg failed funds, delisted companies etc) have been included in the data he or she is relying upon.
Question 8 : Which of the following statements is true in respect of a non financial manufacturing firm? I. Market risk is not relevant to the manufacturing firm as it does not take proprietary positions II. The firm faces market risks as an externality which it must bear and has no control over III. Market risks can make a comparative assessment of profitability over time difficult IV. Market risks for a manufacturing firm are not directionally biased and do not increase the overall risk of the firm as they net to zero over a long term time horizon (a) III only (b) IV only (c) I and II (d) III and IV
The correct answer is choice 'a'
A non-financial firm such as a manufacturing company faces market risks similar to those faced by financial firms, except perhaps for not being exposed to risks from the equity markets. Non financial firms commonly face interest rate risks in respect of their debts, commodity price risks in respect of their inputs and products, and foreign currency risks in respect of their overseas operations. It is therefore not correct to say that the manufacturing firm does not face market risk because it does not take proprietary positions. While decisions on positions may not be actively taken, positions in foreign exchange (eg, through overseas debtors owing foreign currency, or liabilities in foreign currencies to overseas suppliers), commodities (through exposure to the need for raw material and inventory of finished goods) and interest rates (through debt financed, whether at fixed or floating rates) exist and create market risk much in the same way as they would for a proprietary position. Therefore statement I is incorrect. While the firm faces market risks as an externality (as do financial firms for that matter, though often they seek such exposure to profit from their view on which way the externality will express itself), it is incorrect to say that these risks must be borne. They can be measured and hedged. Therefore statement II is incorrect. The results of a manufacturing firm will include gains and losses arising from exposure to market risk, and will cloud the true profitability of the business. A firm with significant unhedged overseas sales may show vastly different results across time periods due to the FX gains and losses, making comparative assessment of profitability difficult. Therefore statement III is correct. Market risks for a manufacturing firm may be directionally biased in terms of exposure, ie there may be a consistent 'long' position in a particular commodity that the firm produces, and a consistent 'short' position in the commodities consumed. In the same way, directional biases may exist in FX or
interest rate exposures too. Regardless of the bias, the existence of market risk exposures increase the volatility of the income stream and make the firm more risky, even though the long term expected returns from such exposures is zero (ie, returns may be zero but standard deviation is not). Therefore statement IV is not correct as market risks form non financial firms do increase the overall risk of the firm.
Question 9 : Which of the following represent the parameters that define a VaR estimate? (a) confidence level, the holding period and expected volatility (b) confidence level and the underlying stochastic process (c) confidence level and the holding period (d) trading position and distribution assumption
The correct answer is choice 'c'
VaR is specified by just two parameters - the holding period, and the confidence level. We speak of, for example, a 10-day VaR at the 95% confidence level. No other parameters are required. Therefore Choice 'c' is the correct answer and the others are incorrect.
Question 10 : In setting confidence levels for VaR estimates for internal limit setting, it is generally desirable: (a) that actual losses very frequently exceed the VaR estimates (b) that actual losses never exceed the VaR estimates (c) that actual losses exceed the VaR estimates on only the rarest of occasions (d) that actual losses exceed the VaR estimates with some reasonably observable frequency that is neither too high nor too low
The correct answer is choice 'd'
If the confidence levels for a VaR estimate are set too high, there may never be any exceedences, ie actual losses will never exceed VaR estimates. For limit setting, we want actual losses to exceed the VaR estimates enough number of times as during the year so that the limits are considered seriously. If the VaR estimate is exceeded too many times, or never, then it is unlikely to be considered seriously. Therefore Choice 'd' is the correct answer. The other answers are incorrect as they either require the VaR to be too high (ie zero or rare excess loss situations) or too low (ie there will be too many cases of excess loss situations to be taken seriously).
Question 11 : Which of the following statements are true: I. It is usual to set a very high confidence level when estimating VaR for capital requirements. II. For model validation, very high VaR confidence levels are used to minimize excess losses. III. For limit
The correct answer is choice 'b'
The minimum multiplication factor specified under Basel II is 3. Therefore the correct answer is Choice 'b'. The exact requirements are laid down below. Each bank must meet, on a daily basis, a capital requirement expressed as the higher of (i) its previous day’s value-at-risk number measured according to the parameters specified in this section and (ii) an average of the daily value-at-risk measures on each of the preceding sixty business days, multiplied by a multiplication factor. The multiplication factor will be set by individual supervisory authorities on the basis of their assessment of the quality of the bank’s risk management system, subject to an absolute minimum of 3. Banks will be required to add to this factor a “plus” directly related to the ex-post performance of the model, thereby introducing a built in positive incentive to maintain the predictive quality of the model. The plus will range from 0 to 1 based on the outcome of so-called “backtesting.” Question 14 : A statement in the annual report of a bank states that the 10-day VaR at the 95% level of confidence at the end of the year is $253m. Which of the following is true: I. The maximum loss that the bank is exposed to over a 10-day period is $253m. II. There is a 5% probability that the bank's losses will not exceed $253m III. The maximum loss in value that is expected to be equaled or exceeded only 5% of the time is $253m IV. The bank's regulatory capital assets are equal to $253m (a) I and IV (b) II and IV (c) III only (d) I and III
The correct answer is choice 'c'
Statement I is not correct as VaR does not set an upper limit on losses. In this case, the bank expects the losses to exceed $253m 5% of the times, and the VaR number does not indicate any theoretical maximum amount of losses. Statement II is incorrect as there is a 95% (and not 5%) probability that the bank's losses will not exceed $253m Statement III is correct and describes VaR. Statement IV is incorrect, as regulatory capital is a more complex computation for which VaR is only one of the various input.
Question 15 : A risk analyst analyzing the positions for a proprietary trading desk determines that the combined annual variance of the desk's positions is 0.16. The value of the portfolio is $240m. What is the 10-day stand alone VaR in dollars for the desk at a confidence level of 95%? Assume 250 trading days in a year.
(a) $6,297, (b) $157,440, (c) $12,595, (d) $31,488,
The correct answer is choice 'd'
The z value at the 95% confidence level is 1.64. Since the variance is 0.16, the annual volatility is 40%. Therefore the daily volatility is 40% x √10/250 = 8%. The VaR therefore is 8% x 1.64 x $240m = $31,488,
Question 16 : For a security with a daily standard deviation of 2%, calculate the 10-day VaR at the 95% confidence level. Assume expected daily returns to be nil. (a) 14.71% (b) 10.40% (c) 2% (d) None of the above.
The correct answer is choice 'b'
If the daily standard deviation is 2%, the 10-day standard deviation will be 2%* √10 = 0.063245. The value of Z at the 95% confidence level is 1.64485. Therefore the VaR value is 1.64485 * 0.063245 = 10.4%. The other choices are incorrect.
Question 17 : If the 1-day VaR of a portfolio is $25m, what is the 10-day VaR for the portfolio? (a) $7.906m (b) $250m (c) $79.06m (d) Cannot be determined without the confidence level being specified
The correct answer is choice 'c'
The 10-day VaR is = $25m x SQRT(10) = $79.06m. Choice 'c' is the correct answer. Question 18 : If the annual variance for a portfolio is 0.0256, what is the daily volatility assuming there are 250 days in a year. (a) 40.48% (b) 0.06% (c) 0.16% (d) 1.01%
The t-distribution is flatter, and actually appears lower than a normal distribution, which may make one think that it has a lower kurtosis and therefore should have thinner tails than a normal distribution. But that is not so, and the "visual" inspection test fails for inferring the kurtosis from just looking a the shape of the distribution. The kurtosis of a t-distribution is given by the formula {
- 6/(d - 4)}, where d is the degrees of freedom and d > 4. Therefore the kurtosis of a t-distribution is always greater than 3 as "6/(d-4)" will always be a positive number being added to 3. Therefore there is no conflict between a t-distribution having fatter tails than a normal distribution as it has a higher kurtosis, even though it appears 'lower' on a graph when superimposed with a normal distribution.
Question 21 : An assumption of normality when returns data have fat tails leads to: I. underestimation of VaR at high confidence levels II. overestimation of VaR at low confidence levels III. overestimation of VaR at high confidence levels IV. underestimation of VaR at low confidence levels (a) II, III and IV (b) I, II, III and IV (c) I and II (d) I, II and III
The correct answer is choice 'c'
When returns are non-normal and have fat tails, an assumption of normality in returns leads to underestimation of VaR at high confidence levels. At the same time, at lower confidence levels the normal distribution may give higher VaR estimates. Therefore Choice 'c' is correct. The other choices are incorrect. Also refer to the tutorial about VaR and heavy tails.
Question 22 : A Monte Carlo simulation based VaR can be effectively used in which of the following cases: (a) Where analytical methods are too complex to effectively use (b) When returns are discontinuous or display large jumps (c) When returns data cannot be analytically modeled (d) All of the above
The correct answer is choice 'd'
Monte Carlo simulations can be effectively used in all cases where an analytical estimate of the VaR cannot be made for any reason - which may include complexity of portfolios, discontinuities or non-linearity in returns or just the plain unavailability of closed form analytical models. Therefore Choice 'd' is the correct answer.
Question 23 : If μ and σ are the expected rate of return and volatility of an asset whose prices are log-normally distributed, and Ψ a random drawing from a standard normal distribution, we can simulate the asset's returns using the expressions: (a) μ + Ψ.σ (b) μ / Ψ.σ (c) -μ + Ψ.σ (d) μ - Ψ.σ
The correct answer is choice 'a'
A standard model for representing asset returns in finance is the Geometric Brownian Motion process, and returns according to this model can be estimated by the expression given in Choice 'a'. Note that prices according to this model are log-normally distributed, and returns are normally distributed. Question 24 : Which of the following are true: I. Monte Carlo estimates of VaR can be expected to be identical or very close to those obtained using analytical methods if both are based on the same parameters. II. Non-normality of returns does not pose a problem if we use Monte Carlo simulations based upon parameters and a distribution assumed to be normal. III. Historical VaR estimates do not require any distribution assumptions. IV. Historical simulations by definition limit VaR estimation only to the range of possibilities that have already occurred. (a) I, III and IV (b) III and IV (c) I, II and III (d) All of the above
The correct answer is choice 'a'
Statement I is true. If a Monte Carlo simulation is based upon the same parameters as used for analytical VaR, and enough number of simulations are carried out, we would get the same results as with analytical VaR. Statement II is false. We cannot use Monte Carlo simulations using parameters based upon a normal assumption when the underlying distribution is not normal. For example, if a return stream is based upon say a uniform distribution, we cannot use a simulation based upon drawings from a normal distribution even though we use the same mean and standard deviation. Statement III is true. This is the advantage of historical simulations - no assumptions are necessary. (Historical simulations however often suffer from the great disadvantage of the paucity of data that would cover all possibilities.) Statement IV is true. The results of historical simulations are limited to the data they are based upon. Question 25 : Monte Carlo simulation based VaR is suitable in which of the following scenarios: I. When no assumption can be made about the distribution of underlying risk factors II. When underlying
The correct answer is choice 'b'
The VaR of a fixed income instrument is given by Duration x Interest Rate x Volatility of the interest rate x z-factor corresponding to the confidence level. For this question, VaR =6 * 10% * 5% * SQRT(10/250) *2.33 * 10,000,000 = $139,800m. Choice 'b' is the correct answer.
Question 28 : The estimate of historical VaR at 99% confidence based on a set of data with 100 observations will end up being: (a) the weighted average of the top 2.33 observations (b) the extrapolated returns of the last 1.64 observations (c) the worst single observation in the data set (d) None of the above
The correct answer is choice 'c'
The VaR in this case will be the top quintile of observations. In this case, since there are exactly 100 observations, this would mean the worst return would become the VaR. Therefore Choice 'c' is the correct answer. Choice 'b' and Choice 'a' make no sense. This highlights that at higher confidence levels, fewer and fewer observations impact the VaR if we are using historical simulation based VaR.
Question 29 : An equity manager holds a portfolio valued at $10m which has a beta of 1.1. He believes the market may see a dip in the coming weeks and wishes to eliminate his market exposure temporarily. Market index futures are available and the current futures notional on these is $50, per contract. Which of the following represents the best strategy for the manager to completely hedge his risk according to his views? (a) Sell 220 futures contracts (b) Liquidate his portfolio as soon as possible (c) Sell 200 futures contracts (d) Buy 220 futures contracts
The correct answer is choice 'a'
The number of futures contracts to sell are equal to $10m x 1.1/$50,000 = 220. Liquidating his portfolio would reduce the beta to zero, but would also get rid of the bets he wants to play on. Therefore Choice 'a' is the correct answer.
Question 30 : When estimating the risk of a portfolio of equities using the portfolio's beta, which of the following is NOT true: (a) relies upon the single factor CAPM model (b) explicitly considers specific risk inherent in the portfolio for risk calculations (c) use of the beta
assumes that the portfolio is diversified enough so that the specific risks of the individual stocks offset each other (d) using the beta significantly eases the computational burden of calculating risk
The correct answer is choice 'b'
Using the beta for VaR calculations is a significant simplification based on the CAPM and the assumption that any specific risks are diversified away. The one thing a risk model based on the CAPM does not consider is the specific risk of individual stocks, because, as mentioned, these are considered to be offsetting each other so that the portfolio only carries market risk reflected in the beta.
Question 31 : For the purposes of calculating VaR, an FRA can be modeled as a combination of: (a) two zero coupon bonds (b) a zero coupon bond and an interest rate swap (c) a zero coupon bond and a floating rate note (d) a fixed rate bond and a zero coupon bond
The correct answer is choice 'a'
A forward rate agreement allows one of the parties to borrow an amount at a rate for a length of time, all of which are agreed in advance. Consider a "3 x 6" FRA. This allows a fixed rate borrowing starting at 3 months till the end of 6 months. This is economically equivalent to holding a zero coupon bond till the end of 6 months, and being short another zero coupon bond till the end of 3 months (or the other way round, depending upon which end of the FRA you are on). Therefore Choice 'a' is the correct answer.
Question 32 : When the volatility of the yield for a bond increases, which of the following statements is true: (a) The VaR for the bond increases and its value decreases (b) The VaR for the bond decreases and its value increases (c) The VaR for the bond increases and its value stays the same (d) The VaR for the bond decreases and its value is unaffected
The correct answer is choice 'c'
The VaR of a fixed income instrument is given by Duration x Volatility of the interest rate x z-factor corresponding to the confidence level. Therefore as the volatility of the yield goes up, the value at risk for the instrument goes up. At the same time, the value of the bond is given by the present value of its future cash flows using the current yield curve. This value is unaffected by the volatility of the underlying interest rates. Therefore a change in volatility of interest rates does not affect the value of the bond.
The correct answer is choice 'b'
The second order approximation of the VaR of an options position is given by [Option delta x Underlying's VaR - Option gamma/2 x (Underlying's VaR)^2]. Therefore, a higher gamma reduces VaR and a lower gamma increases VaR. Hence Choice 'b' is the correct answer.
Question 36 : The backtesting of VaR estimates under the Basel accord requires comparing the ex-ante VaR to: (a) the Basel accord does not require banks to backtest VaR estimates (b) realized profit and loss for the period (c) hypothetical profit and loss keeping the positions constant (d) ex-ante VaR calculated for the subsequent periods
The correct answer is choice 'b'
Basel II requires financial institutions to compare their ex-ante VaR estimates to actual realized P&L. Therefore Choice 'b' is the correct answer. A bank may use hypothetical P&L based upon constant positions to validate its model, but that is not required for Basel II.
Question 37 : Ex-ante VaR estimates may differ from realized P&L due to: I. the effect of intra day trading II. timing differences in the accounting systems III. incorrect estimation of VaR parameters IV. security returns exhibiting mean reversion (a) I, II and IV (b) I, II and III (c) II, III and IV (d) I and III
The correct answer is choice 'b'
Ex-ante VaR calculations can differ from actual realized P&L due to a large number of reasons. I, II and III represent some of them. Mean reversion however has nothing to do with VaR estimates differing from actual P&L. Therefore Choice 'b' is the correct answer.
Question 38 : Which of the following cannot be used to address the issue of heavy tails when modeling market returns (a) Student's t-distribution (b) EWMA (c) Normal mixtures (d) EVT
The correct answer is choice 'b'
Normal mixtures, EVT and the t-distribution are all possible solutions addressing the issue of heavy tails in financial returns. EWMA and GARCH address volatility clustering, which is the other problem when doing risk calculations. Therefore Choice 'b' is the correct answer as EWMA is not used to address heavy tails but volatility clustering.
Question 39 : For an equity portfolio valued at V whose beta is β, the value at risk at a 99% level of confidence is represented by which of the following expressions? Assume σ represents the market volatility. (a) 2.326 x V x σ / β (b) 2.326 x β x V x σ (c) 1.64 x β x V x σ (d) 1.64 x V x σ / β
The correct answer is choice 'b'
For the PRM exam, it is important to remember the z-multiples for both 99% and 95% confidence levels (these are 2.33 and 1.64 respectively). The value at risk for an equity portfolio is its standard deviation multiplied by the appropriate z factor for the given confidence level. If we knew the standard deviation, VaR would be easy to calculate. The standard deviation can be derived using a correlation matrix for all the stocks in the portfolio, which is not a trivial task. So we simplify the calculation using the CAPM and essentially say that the standard deviation of the portfolio is equal to the beta of the portfolio multiplied by the standard deviation of the market. Therefore VaR in this case is equal to Beta x Mkt Std Dev x Value x z-factor, and therefore Choice 'b' is the correct answer.
Question 43 : What is the 1-day VaR at the 99% confidence interval for a cash flow of $10m due in 6 months time? The risk free interest rate is 5% per annum and its annual volatility is 15%. Assume a 250 day year. (a) $85, (b) $5, (c) $109, (d) $1,744,
The correct answer is choice 'b'
(c) Proportional to the inverse of the square root of the sample size (d) None of the above
The correct answer is choice 'c'
When we do a Monte Carlo simulation, the statistic we obtain (eg, the expected price) is an estimate of the real variable. The difference between the real value (which would be what we would get if we had access to the entire population) and that estimated by the Monte Carlo simulation is measured by the 'standard error', which is the standard deviation of the difference between the 'real' value and the simulated value (ie, the 'error'). As we increase the number of draws in a Monte Carlo simulation, the closer our estimate will be to the true value of the variable we are trying to estimate. But increasing the sample size does not reduce the error in a linear way, ie doubling the sample size does not halve the error, but reduces it by the inverse of the square root of the sample size. So if we have a sample size of 1000, going up to a sample size of 100,000 will reduce the standard error by a factor of 10 (and not 100), ie, SQRT(1/100) = 1/10. In other words, standard error is proportional to 1/√N, where N is the sample size.
Question 48 : The accuracy of a VaR estimate based on a Monte carlo simulation of portfolio prices is affected by: I. The shape of the distribution of portfolio values II. The number simulations carried out III. The confidence level selected for the VaR estimate (a) I, II and III (b) II (c) II and III (d) III
The correct answer is choice 'a'
VaR calculations look at the lower part of the distribution of future portfolio values, for example, if the desired confidence level is 95%, the cut-off for the VaR calculation will be at the bottom 5%; similarly at 1% for a 99% confidence level. The number of observations that will end up in these bottom ranges will be few and sparse, and therefore their accuracy will generally be lower than, say, the average where observations are more likely to be concentratred. If the shape of the distribution of future portfolio values is not symmetrical and has a long tail to the left, then this problem gets further exacerbated as there may be even fewer and less reliable simulated numbers at the 5% or 1% quintiles. Thus the shape of the distribution will affect the accuracy of a VaR estimate. The distribution for a short option position, for example, will have a long tail to the left, and the VaR number will be quite significantly affected by a few simulations. On the other hand, for a long option position where the long tail is to the right, and we are interested in the left tail which is better defined and ends at zero we are more likely to get a better VaR estimate. Therefore Statement I is correct.
The number of simulations carried out directly affects the standard error, which is inversely proportional to the square root of the sample size (ie the number of simulations). THe accuracy of the VaR estimate can be increased by increasing the sample size (or reduced by reducing the sample size). Therefore Statement II is correct. The confidence level selected for the VaR estimate also affects the accuracy of the estimate. To intuitively understand this, consider this extreme example where the desired confidence level is 99.9% and there are 1000 observations. Therefore the VaR will be determined by the last value in the sample, and will therefore be quite fickle and dependent upon what chance produces as the lowest value in the simulation. But if for the same sample the confidence level desired were to be 90%, there would be 100 observations beyond the 90% cut-off and this would be a much more stable and accurate number. Therefore the confidence level selected for the VaR estimate is also a determinant of the accuracy of the VaR estimate derived from the simulation. Statement III is correct.
Question 49 : Which of the following introduces model error when basing VaR on a normal distribution with a static mean and standard deviation? (a) Volatility clustering (b) Heavy tails (c) Autocorrelation of squared returns (d) All of the above
The correct answer is choice 'd'
When VaR is based on an assumption of normality with a static mean and volatility, it means anything that violates these assumptions will introduce model error. Volatility clustering implies a non-static volatility. Heavy tails imply non-normality of the shape of the distribution. Autocorrelation of squared returns implies that returns are not independent and identically distributed. Therefore all of these introduce model error. Choice 'd' is therefore the correct answer.
Question 50 : As the persistence parameter under EWMA is
lowered, which of the following would be true:
(a)The model will react slower to market shocks (b)High variance from the recent past will persist for longer (c)The model will give lower weight to recent returns (d)The model will react faster to market shocks
The correct answer is choice 'd'
The persistence parameter, λ, is the coefficient of the prior day's variance in EWMA calculations. A higher value of the persistence parameter tends to 'persist' the prior value of variance for longer. Consider an extreme example - if the persistence parameter is equal to 1, the variance under EWMA will never change in response to returns.
