Hi,
I have two doubts that probably you can give me a hand.
a) There is portfolio of Interest Rate deposits, so I do not have prices, I have interest rates. So, I can use the Ln (Logarithm ), or it is just fine leaving as they are . AT the end of the day they are already the returns of the underlying.
However, missing the Ln factor my curve is not going to be nice. I read in other blog that this is not accurate. Any one has any idea?
b) Any one has an example to calculate the Linear Parametric for a portfolio?
Many thanks,
Daniel
Replies
Thanks to everyone!!
Now, I have more clarity and I'll think that the model should adjust with the hints you gave me for a fatter tails distribution.
I think is the best solution due to the fact of the manipulation of the rates by the Central Banks.
Frank I totally agree. I suggest all risk managers read this article http://hedgefundvet.blogspot.com.
Given where interest rates are at the moment - close to zero - none of the historical methods are up to giving reasonable values of VaR. This is an area where we need to do proper risk management by scenario testing.
If an archaic system, or your compliance group (sometimes the same thing), really do want a VaR then do something simple to give you a number that is roughly right. That is really the best you can do at the moment!
Don't sweat the small stuff.
Regarding question a), the issue is whether interest rates have a "normal" behavior or a "log-normal" one. In other words, whether their volatility is independent of the level or, on the contrary, proportional to it (regardless of "fat tails" which are another issue). As fixed income assets are, broadly speaking, valued like exp(-r*D) where r is the interest rate and and D is the duration, if the volatility of rates is independent of the rate, then the price is, like an equity price, "log-normal" (still with quotes, disregarding the fat tail question), and the price volatility is the interest rate "normal volatility", multiplied by the duration. But if the rates are "log-normal", then the price volatility is, on top of that, proportional to the level of rates.
I have written an extended note on this question, which you can find on Riskdata website www.riskdata.com. To summarize it, when rates are medium or high, say above 5%, their volatility is proportional to the level, i.e. "log-normal" model, but with the current low rate configuration (even possibly negative), they behave like "normal". One can encompass both situations by shifting the 0 to -1%. In other words, the rates volatility is proportional to (rate + 1%). And this is valid across all economic periods and countries (analysis done including the 70's). In the current context, the only danger of using a strict "normal" model of interest rates (or, equivaently, a "log-normal" model of prices) is fat tails: in case of a sudden IR surge, the regime will change and the volatility will surge together with the rates.
Regarding question b), can you be more precise about what is a "linear parametric"? Sorry this is probably a simple notion and I just don't know this wording. Are you talking of the VaR computed using a multilinear factor analysis of the portfolio, knowing the covariance matrix of the factors?
In this case, the first thing is to deduce from multi-factor betas and factor covariances the variance of the portfolio. If:
Ptf_return = Sum(Beta(k)*Fact(k))
Covar(Fact(k), Fact(j)) = Ckj (including Variance(Fact(k)) = Ckk)
Then Variance(Ptf_return) = Sum_over_all_pairs_kj(Ckj*Beta(k)*Beta(j)) = Sum(Ckk*Beta(k)^2) + 2 Sum_over_k<j(Ckj*Beta(k)*Beta(j))
Note that Ckj = StDev(Fact(k)) * StDev(Fact(j)) * Correl(k,j)
Finally StDev(Ptf_return) = Sqrt(Variance)
VaR(Ptf) = Multiplier * StDev(Ptf_return) * Ptf_NAV
In a Gaussian model, the multiplier is NormSInv(Quantile), e.g. 2.33 for the 99% VaR. However, it is recommended to increase this multiplier to account for fat tails, e.g. 3 or 3.5 for the 99% VaR.
Hope my answer helps.
Hi Daniel,
Could you provide me what kind of statistics you would like to do or study you would like to run on the interest rates curves?
I could help you if you give me more details.
Many thnaks.
Check if this link might be of any help
http://home.ubalt.edu/ntsbarsh/business-stat/otherapplets/PaRHSSyEq...
Daniel,
If you are trying to verify that the amounts reported are correct then you should generally be able to verify that the interest rates being used are accurate by tracing those back to the sources they are linked to (i.e LIBOR). If you start with your beginning balance you should be able to verify that the ending balance is accurate by doing some simple math if that is what you are trying to accomplish here.