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Nov 24, 2024
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Fin285a Page 1 of 9 Final Exam: Fall 2014 NAME: (write your name here!!) FIN285a: Computer Simulations and Risk Assessment Final Exam: Tuesday, December 16
th
Fall 2014: Professor B. LeBaron Directions: Answer all questions. You have 3 hours. Point weightings are listed next to each problem. There are 100 points total. Answer what you know first, and then go back to other problems. Stay calm, and good luck. Part I: Interpreting matlab code: In the following problems you will be asked to interpret some example matlab programs. 1. (3 points each part) What is the output of the following matlab programs: a.) x = 1:10; find(x<5) [1 2 3 4] b.) cumprod(2:2:4) [2 8] c.) gpcdf(0,1/5,5) 0 d.) a = [1 2]; w = [0.5 0.5]; a*w’ 1.5
Fin285a Page 2 of 9 Final Exam: Fall 2014 2. (12 points) Answer this question referring to the following matlab code: load sp500.dat; % one day price level to p p = sp500(:,2); ret1 = (p(2:end)-p(1:end-1))./p(1:end-1); mu = mean(ret1); [vols, range] = ema((ret1-mu).^2, 0.96, 500); vols = vols(range);ret1 = ret1(range);stds = sqrt(vols); stdret = (ret1-mu)./stds; rstar = quantile(stdret,0.01); rt = rstar*stds+mu; var = 100 –
100*(1+rt); ex = (ret1<rt); mean(ex)
a.) What is rt? Is it a number or a vector? Vector of return critical values adjusted for changing volatility levels. b.) What does the variable ex represent here? VaR exceptions c. If the model is working correctly what value should the last line be printing (approximately)? 0.01 d.) Is this model assuming that standardized returns are normally distributed (yes or no)? No, uses actual standardized returns.
Fin285a Page 3 of 9 Final Exam: Fall 2014 3. (12 points) Answer this question referring to the following matlab code:
% ret1 are one day log returns h = 40; for i = 1:100000 ret1bs = sample(ret1,h) port40daysbs(i) = prod(exp(ret1bs))*100; end var1 = 100-quantile(port40daysbs,0.01); index = 1:nsamp-(h-1); for i = 1:100000 start = sample(index,1); ret1bs = ret1(start:startt+(h-1)); port40daybs(i) = prod(exp(ret1bs))*100; end var2 = 100-quantile(port40daysbs,0.01); a.) Does the first for loop and VaR calculation assume that returns are normally distributed (yes or no)? no b.) Does the first for loop assume that returns are independent over time (yes or no)? yes (it is an independent bootstrap) c.) What type of bootstrap is the second loop doing? Block bootstrap d.) In our examples from class which of the two VaR measures (var1 or var2) was larger? Var2
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Fin285a Page 4 of 9 Final Exam: Fall 2014 4.) (12 points)Answer this question referring to the following matlab code: rdaily = rannual/250;startspread=10;stopspread=1; for i=1:niterat [p1, p2] = pairsgen(ndays,startspread); shares1 = 100/p1(1); shares2 = 100/p2(1); dist = p2-p1; stopdate = find(dist<stopspread); if(all(dist>stopspread)) stopdate = ndays; else stopdate = stopdate(1); end val(i) = (shares1*p1(stopdate)-shares2*p2(stopdate)/... (1+rdaily*stopdate); mmkt = shares1*p1 - shares2*p2; liq(i) = min( mmkt(1:stopdate)); end quantile(val,0.01) quantile(liq,0.01) a.) What does the variable “
stopspread
”
represent here? Price criterion for stopping the strategy when prices get close. P2-P1<1. b.) Can stopdate be a vector, and if so why do we only care about stopdate(1) in this program? Yes, it would be all the dates where the prices are close. Only the first one matters for the strategy. c.) Which variable tries to replicate potential intermediate cash flows on this long/short position? nmkt d.) Why is discounting val with the interest rate important in this problem? The strategy may take different times to run under different simulations. To be able to compare the final values present value calculations must be done.
Fin285a Page 5 of 9 Final Exam: Fall 2014 Part II. Multiple choice (3 points each)
: Circle the one best answer from the choices. 5. Our pairs trading example showed that >a.) intermediate cash flows can be very risky, even when the final outcome of the portfolio looks safe. b.) VaR completely measured pairs trading risk. c.) market neutral strategies are immune to any risk. d.) good trading pairs can be hard to find. 6. VaR exceptions that are clumped together over time are probably an indication that a.) the return distribution is normal. b.) extreme values distributions will work. >c.) you are not modeling changing variances correctly. d.) portfolio changes are not correctly included in the VaR calculation. 7. The unconditional
distribution of GARCH model generated returns is a.) normal. b.) Generalized Pareto. c.) skewed. >d.) fat tailed. 8. The volatility term structure refers to a) volatility of interest rates at different horizons >b.) the dynamic pattern of predicted asset return volatility going into the future c.) VaR levels at different interest rates. d.) interest rate spreads for different volatility levels. 9. Estimating a Generalized Pareto Distribution GPD gives an estimate of the tail exponent. This value tells you a.) which moments exist. b.) a relationship between VaR and expected shortfall. c.) the slope for linear scaling relationships in log/log plots. >d.) all of the above. 10. In our example with US and UK stocks and a put option placed on the US component, we saw that the distribution of final portfolio values was a.) normal. >b.) skewed. c.) thin tailed and symmetric.
Fin285a Page 6 of 9 Final Exam: Fall 2014 d.) not important to VaR estimation. 11.) You have evaluated VaR on a portfolio with several stocks and an at –
the-money put option on one of the stocks. The option value is obtained from the current market price. The market price of this option increases, but nothing else changes. Your new estimate of VaR will a.) not change. b) go down. >c) go up. d) not enough information to tell. 12.) Delta-normal VaR calculations can have problems even when returns are normal because >a.) the valuation functions are nonlinear. b.) the valuation function is linear. c.) the portfolio weights can be negative. d.) normal tables can be inaccurate. 13.) The distribution of total investor wealth at long horizons with independent returns shows the following feature. >a.) the mean wealth exceeds the median wealth. b.) the median wealth exceeds the mean wealth. c.) the distribution has a long left tail. d.) the mean wealth equals the median wealth. 14.) In the article we read titled, “
What Can We Learn from Prior Periods of Low Volatility?
”
the authors describe conditions during the low volatility periods in the summer of 2014, and the period in May 2007 proceeding the financial crisis. Their conclusion was that a) market characteristics in these two periods were very similar. >b) market characteristics in these two periods were very different. c) there was a lot of key information that would forecast the impending financial crisis of 2008. d) financial volatility can be used to predict t-bill spreads.
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Fin285a Page 7 of 9 Final Exam: Fall 2014 Part III. Very short answer. Answer the following with numbers or a few words. 15. (10 points) Consider a world where the daily log return for your portfolio follows a normal distribution with mean 0, and standard deviation, s. Log returns are independent over time. a.) What is the std for the 9 day log return? 3s b.) Can you write down a matlab expression for the 9 day VaR from this information for a portfolio with a starting value of 100? (Hint: This might require functions like log, quantile, norminv, or exp.) 100 – 100*exp( norminv(0.01, 0, sqrt(9)*s)) 16. (5 points) Assume returns follow a power-law distribution in their extreme tails with a tail exponent of . If the probability of returns being less than -0.02 is 0.04, then what is the probability of returns being less than -0.04?
Fin285a Page 8 of 9 Final Exam: Fall 2014 17. In the GARCH(1,1) model people often measure the conditional variance in terms of its deviation from the long run variance. , Reminder on the GARCH(1,1): a.)
(2 points) Assume you are at time t-1, and you know all returns up to t-1, and all conditional variances through t-1. Can you find with your information (why or why not)? (You also know all the model parameters.) You know everything on the right hand side at time t-1. b.)
(2 points) Write down an expression for a forecast of using only things you know at t-1 and model parameters.
Fin285a Page 9 of 9 Final Exam: Fall 2014 c.)
(3 points)What is the ratio of the forecast for using only time t-1 information, divided by as a function of the model parameters and j?
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