Fixed Income Portfolio Management - Master thesis topic

[PMFI]

Hi all,

I am going to start an internship in fixed income portfolio management.

I will write my master thesis at that time:
Do you have any suggestions for an interesting topic in that field ?
If you can also refer to some papers, it would be great

Thank you !

 

[Tsotne]

Refer to the following thread and tell me if interested in that opinion I posted about the dependence structure in Markotitz portfolio. Instead of using correlation matrix, using copula functions (still thinking how).

http://www.quantnet.com/forum/threa...-hedge-fund-manager-scott-vincent.6750/unread

 

[Shantanu Kumar]

I may be a bit off topic but i need to clarify something regarding copula.
Isn't the idea of copula bit misleading to identify the dependencey between random variables as in case of copula we assume that the certain kind of joint distribution.So if we change the type of copula ,distribution changes.
Basically we are just assuming certain kind of dependency or do we have certain idea beforehand.

 

[Tsotne]

What you said above is a bit unclear for me. I believe in "dependency has distribution" you mean joint distrbution. Yes sure they have and that's the catch. If you find the marginal distributions and connect the logarithmic returns of stocks by some copula, you'll be able to recover the stock prices themselves by simulating increments (log returns) into any T horizon. That definitely gives better dependency structure with rich toolbox of dependency characteristics that copulas hold than miserable linear pearson correlation coefficient. How to connect the risk-return for optimization purposes is another topic and deserves to be thought about.

 

[Shantanu Kumar]

Yes i meant the joint distribution.
So copulas are just an improvement over pearson correlation cofficient.We can't really argue for their credibility or can we?

 

[Tsotne]

Yes i meant the joint distribution.
So copulas are just an improvement over pearson correlation cofficient.We can't really argue for their credibility or can we?

Copulas are not improvement over pearson rho. They are the most powerful measurer of dependence between random variables. Pearson's rho is a quick, dirty (and what is nightmare - linear) measurer of dependence.As for credibility, I'm still unsure what you mean...credibility in what sence? All the parameters in copula functions which determine the strength of dependence is into your hands. Optimize it to maximally approach the right copula. According to Sklar's theorem: If X1 and X2 are the random variables with marginal distributions X1~F and X2~G and have joint distribution function H(x1,x2), then there is a copula C[F(x1),G(x2)] for those random variables and vise versa. Moreover, if marginals are continuous, C is unique. Take a look at the parametric families of copulas like Archimedean copulas and optimize the theta parameter to approache the true copula. Is that what you mean in credibility?

 

[Shantanu Kumar]

By credibility i was trying to emphasize that selection of a particular kind of copula is somewhat random.Is there any theory dedicated to the selection of copula? We just choose something which we find easy to interpret and implement.Can we say that in a particular case a particular kind of copula will work better over another kind of copula?
Consider the scenario where two random variables are independent, we can still find a copula for their joint distribution.Right?

 

[Tsotne]

By credibility i was trying to emphasize that selection of a particular kind of copula is somewhat random.Is there any theory dedicated to the selection of copula? We just choose something which we find easy to interpret and implement.Can we say that in a particular case a particular kind of copula will work better over another kind of copula?

Of course you can. As you behave in marginal distribution where you are checking the hypothesis whether X or Y separately have one particular marginal distribution, you do the same in copulas. Fitting copula is nothing more than finding the joint distribution of uniformly distributed marginals over the interval [0,1]. Check Chi-Square test and Kolmogorov-Smirnov test for selection both with copulas and marginals. The only difference in Chi-Square test for multidimensional copulas is that you have bins of space on 3D histograms(depending on dimensions, if more than you got imaginary histogram of n dimensions) Likewise in Kolmogorov-Smiornov test is applied whether the checked copula is rejected or not. Once you get the test value (see kolmogorov and Chi-Square) of test, you are comparing it against Chi quantile (Chiinv) as normal.

 

[Shantanu Kumar]

Even though i had heard about copulas and all during my university i never worked with them.Very recently i got involved with it.So still a lot to know.
Thank you @Tsotne.That was really helpful.