Can you please tell me what is the difference between calculating the correlation between the prices of 2 assets and between the returns of the prices of these 2 assets?Thanks

well, I think the answer is more or less within the questioncorrelation(X,Y)=cov(X,Y)/[std(X) std(Y)]with cov(X,Y)=E(XY)-E(X)E(Y) and std(X)=sqrt{cov(X,X)}now if X and Y are two asset prices it's one thing and if they are returns another ...but perhaps you are asking that havingdS/S = r dt + sigma dXdP/P = k dt + sigma' dX'when we talk about correlation of X,X' which one it is?for a Log-Normal process it's the continuously compounded returns, since [ln(S/So)-mu.t ]/sigma = X[ln(S/So)-mu'.t]/sigma' = X'with mu = r-1/2sigma^2 ...am I answering your question at all?

not quite... I mean we say ie that Ftse is correlated with S&P and in fact we mean that the correlation between the returns of these 2 indices is high. Why dont we care about the correlation between the levels of these 2 indices? What is the meaning of the correlation of the returns vs the correlation of the leves? Also in VaR calculations when Riskmetrics calculates correlations it refers to returns calculations... why?

the index prices and the stock prices are log-normally distributed which means their (continuously compounded) returns are normally distributed, that's why we look at the correlation between returns and not prices ...makes ense?

Yes the standard correlation measure is based on assumption of normal distributed data. Also your profit/loss (in $) is dependent on price changes/returns "not" on level.An interesting question is naturally how good is standard correlation measure if we have fat tails, jumps etc? What about non-parametric correlation measure: Sperman Rank? But, then most option models assume log-normal assets (normal returns)....so not good to mix sperman rank type corr with log-normal models I would think?

I heard that the Merril equity guys had implemented a "non-linear" correlation, observing that during large moves, everything is highly correlated, but during typical days, things might be nearly uncorrelated. I heard Jim Gatherall's name in connection with this topic. Wish I had the details.

gemikon, we do care about correlation between the levels of FTSE and SPX. For example if we are making a convergence trade. But that may be better measured by cointegration than correlation. Anyway, I think that correlation between returns is nonsense. It's another case of putting the cart before the horse, mathematicians with little imagination use a tool they understand rather than create something more appropriate. Pat, I've been using such a nonlinear correlation since I was in short trousers! Haven't you heard of the "Rings of Saturn"? Plot return of one stock against another. In the middle there's a roundish cloud of dots, with more dots along a 45 degree (or whatever) line. The question is how to use this. I've been playing with a jump-diffusion multi-asset model where correlations are all zero. But the crash bit looks likeV(S_1,S_2,...,t)-V(J a_1 S_1, J a_2 S_2,...,t)with some distribution for the J and the a's being constant, different for each stock, the crash coefficients.P

Paul,A cool and relevant thing to look at is vega hedging. A firm might be buying and selling equity options and accumulate a large amount of vega exposure, which they hedge using index options. However, the correlations between the implied vols (based on daily returns or increments) are negligible. I am starting to work on rationalizing the hedge with Stan Pliska (an academic, I'm afraid).Hari

Stan's a very nice man. Say Hi to him for me!P

if correlation is such a weak measure (i.e. not robust) statistically, does that not throw a lot of doubt on CAPM?

your post was from some time agp, but you might still be interested in this topic.I too have found that implied vol correlations based on daily increments are generally weak, whether stock against index or index against index. There only seems to be a significant correlation in periods of large downward moves (high vol). I guess all this just indicates that it's easier to hedge against broad market volatility over stock-specific volatility.In the example you mentioned, the firm that runs an options book would probably have a well diversified set of names in their portfolio, although they might be biased towards long/short put/call respectively. Why wouldn't you hedge the large individual vega positions with corresponding options in those names, and the residual vega with some index option? An alternative would be to use options on a sector index that matches a subset of your portfolio. Some traders even suggest that if they had to pick between any of the greeks, they would hedge their net theta first, thereby compensating or change in vol.Any thoughts?

Can someone tell me where I can get some very basic reading material on implied/realized correlations? Preferably something regarding stock vs. index. Thx.

Hi,1) Could someone define what is meant by Non-linear correlation? 2) Can we consider instantaneous correlation as a 'process'? Does it have any statistical property?Thank you very much.

Two random variables have linear correlation if E(Y|X) is a linear function of X. The correlation is non-linear if the function of X is non-linear. For example height and weight of adults are correlated, tall people tend to weigh more than short people. But the relation is non-linear, weight tends to go up with the square of height.One financial example of this is that assets tend to have higher correlations in market crashes than in normal times. If you do not adjust for this fact you can get seriously misleading risk assessments. In principle you can regard correlation coefficient as following some sort of stochastic process. However, I don't know of any useful financial models that do this.

Thank you very much Aaron. This is very interesting point. I will have closer look at it and come back for more discussion.