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Chapter 2 Returns. Chapter 3 Fixed Income Securities. Chapter 4 Exploratory Data Analysis. Chapter 5 Modeling Univariate Distributions. Chapter 6 Resampling. Chapter 7 Multivariate Statistical Models.
Chapter 8 Copulas. Chapter 9 Time Series Models: Basics. Chapter 11 Portfolio Theory. Chapter 12 Regression: Basics.
Chapter 13 Regression: Troubleshooting. Chapter 14 Regression: Advanced Topics. Chapter 15 Cointegration. Chapter 17 Factor Models and Principal Components. Chapter 19 Risk Management. Chapter 21 Nonparametric Regression and Splines. John L. For some of the problems I used R to perform any needed calculations. The code snippets for various exercises can be found at the following location:. If you feel that that there is a better way to accomplish or explain an exercise or derivation presented in these notes; or that one or more of the explanations is unclear, incomplete, or misleading, please tell me.
If you find an error of any kind — technical, grammatical, typographical, whatever — please tell me that, too. See the R script Rlab. R where the problem for this chapter are worked. We notice that these returns do appear to be correlated they are distributed somewhat symmetrically about a line and the outliers of each stocks return do appear together.
In the accompanying R code we plot the two returns. They have a correlation using the R function cor given by 0. I get that the hedge fund will make a profit with a probability of 0. I get that the hedge fund will suffer a loss with a probability of 0. I get that the hedge funds expected profit is given by Part b : In five trading days our log return will be normally distributed with a mean 5 0. Thus in this case we need to evaluate. This will happen with a probability of.
For this problem we will need to recall the definitions of the net return. Part a : With dividends our single period gross return is given by. Part b : Next recall that with dividends the multiperiod gross returns R t k are given by.
Part a : The variable r t 4 would be a normal random variable with a mean 4 0. Part b : We would compute this using the R command. Thus we have that. Then since the transformation from R to X k is a monotone transformation the quantiles of R transform to the quantiles of X k using the same monotone transformation.
Thus finding the 0. Given this we find the 0. Part d : Now X k 2 is equal to. The expectation of this is given by integrating the above against the density. Lets now evaluate the integral above dropping for now the coefficient we have. Putting back the factor of we get. Part e : Now we want to compute Var which we do using. Thus we use this formula we need to compute E [ X k ]. Following the same procedure as used above to compute E [ X k 2 ] we get.
In 20 days the log return should be a normal random variable and have a mean value of 20 0. The probability we have a return larger than the above and a final price greater than is given by. When we run the given Rlab. There we see graphically that the value found by the spline function which was 0. The given code with the uniroot function finds the root of the given function.
In this case that is equivalent to finding the square root of 0. There we see that the yields seemed to get smaller as time progressed. There we see the same behavior in that the yield gets smaller as time progresses.
There we see that the yields seemed to get smaller in value as time progressed. Part b : As the bond is selling above par value, the yield to maturity is smaller than the current yield and thus is below 2. The price of this bond will be given by. Using this we see that the left-hand-side of the given expression becomes. Part a : When the bond is issued the annual interest rate is 8. Part b : The semiannual interest rate now is 3. After two coupons payments and with the new interest rates the bond is now worth.
Since the coupon rate is larger than the current yield of 0. Part c : The yield to maturity is less than the current yield since the bond is selling above par. For this we first compute the yield to maturity y 15 which is given by.
The yield to maturity with this continuous forward rate r t is given by. Again the yields had to change since one year has passed and get incremented by 0. Part d : We will compute the rate of return for each of these three investments under the case where the analyst is correct and we find. Thus the investment in the one year zero bond is the only investment that is profitable. Part e : We will compute the rate of return for each of these three investments under the case where the analyst is not correct and we find.
Thus the investment in the three year zero bond gives the largest return. Part f : The bond with the highest spot rate is the five year bond. From the previous part we see that when the spot rate does not change and we sell our bond a year later we get a rate of return of 0.
This however is smaller than the three year bond which under the same situation would give a rate of return of 0. We then get that the derivative of DUR as the spot yield changes is then. It would be worked in the same way.
For example we have. The price of the bond is the sum of these parts or The calculations for this problem are worked in this small R code. Problem EuStockMarkets. These time series look stationary but the fluctuations appear to get larger at certain periods of time again the more recent dates. From that plot we see that none of the indices have returns that look normal.
All of them have heaver tails than a normal distribution would predict. The other three indices appear to be skewed to the left indicating that the negative samples can be larger than the positive samples.
The Shapiro-Wilks test assumes that the input data comes from a normal distribution. The test statistics is the value of W and the p -value is the probability we get a W test statistic this extream from random fluctuations. All of the p -values are very small indicating that we can reject the null hypothesis and conclude that the data does not come from a normal distribution. The code q. The code qt q. The paste command combines multiple strings together into a single string.
Both of the parametric models seem to have tails that fall to zero faster than the empirical density. This would indicate that they will underestimate the probabilities of extream events. Because of this the parametric models have sharper peaks near the zero return origin. We can see that the solid curve the KDE approximation is above the other two curves indicating that the parametric densities under estimate the true density in this range of returns.
Information about this can be given by looking at the results of the online help for bw. The default kernel is the Gaussian kernel. R where the exercises for this chapter are worked. Part a : We can use the summary command to compute some of these statistics.
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Chapter 2 Returns. Chapter 3 Fixed Income Securities. Chapter 4 Exploratory Data Analysis. Chapter 5 Modeling Univariate Distributions. Chapter 6 Resampling.
Matteson is very useful for Mathematics Department students and also who are all having an interest to develop their knowledge in the field of Maths.
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up. I realize that the statistical analysis of financial data is a huge topic, but that is exactly why it is necessary for me to ask my question as I try to break into the world of financial analysis. As at this point I know next to nothing about the subject, the results of my google searches are overwhelming. Many of the matches advocate learning specialized tools or the R programming language. While I will learn these when they are necessary, I'm first interested in books, articles or any other resources that explain modern methods of statistical analysis specifically for financial data.
David Ruppert is the Andrew Schultz, Jr. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics and a winner of the Wilcoxon Prize for the best practical applications paper in Technometrics. He has published over 80 scientific papers and three books, Transformation and Weighting in Regression, Measurement Error in Nonlinear Models, and Semiparametric Regression. If you have any interest or involvement with statistics in financial applications, I recommend this book to you. The book is well-written and clear For the statistician, this is a very good book to peruse, because it presumes no background in finance.
This service is more advanced with JavaScript available. Front Matter Pages i-xxvi. Pages Fixed Income Securities. These methods are critical because financial engineers now have access to enormous quantities of data. To make use of this data, the powerful methods in this book for working with quantitative information, particularly about volatility and risks, are essential.
Springer Texts in Statistics. David Ruppert. David S. Matteson. Statistics and Data. Analysis for Financial. Engineering with R examples. Second Edition.
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ReplyFront Matter. Pages i-xxi. PDF · Introduction. David Ruppert. Pages · Probability and Statistical Models. David Ruppert. Pages · Returns. David Ruppert.
ReplyThis textbook emphasizes the applications of statistics and probability to finance. Students are assumed to have had a prior course in statistics, but no.
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