# [R-SIG-Finance] making sense of 100's of funds

Wed Aug 22 15:19:45 CEST 2007

```My two cents come in the form of an R-script:

# Germany vs USA
dax <- get.hist.quote(instrument = "^gdaxi", start = "1980-01-01", quote
= "Close")
sp <- get.hist.quote(instrument = "^gspc", start = "1980-01-01", quote =
"Close")

# Synchronize data
x <- merge(dax, sp, all=F)

# Avoid synchronization problems due to trading in different time zones
dax <- embed(as.vector(diff(log(x[,1]))), 5)
dax <- apply(dax, 1, sum)

sp <- embed(as.vector(diff(log(x[,2]))), 5)
sp <- apply(sp, 1, sum)

# Compute running correlation with a quaterly window
cov <- apply(embed(sp*dax, 60), 1, mean)
s1 <- sqrt(apply(embed(dax^2, 60), 1, mean))
s2 <- sqrt(apply(embed(sp^2, 60), 1, mean))
cor <- cov/(s1*s2)
idx <- 1:length(cor)

# Plot running correlation over time and loess average
# Correlation increases over time which is not surprising
# with today's levels of globalization
plot(idx, cor, type="l")
lines(idx, predict(loess(cor~idx)), col="green")

# Plot running correlation vs running volatility and loess average
# Correlation is higher during volatile periods, i.e., during market
corrections
plot(s1, cor)
lines(s1, predict(md <- loess(cor~s1)), col="green")

# Plot running correlation vs running volatility and loess average
# Correlation is higher during volatile periods, i.e., during market
corrections
plot(s2, cor)
lines(s2, predict(loess(cor~s2)), col="green")

# Correlation increase over time is somewhat down-biased in the past few
years
# as the past few years exhibited exceptionally low volatility
# Plot running correlation over time with a "bias-corrected" running
correlation
# correcting for different levels of volatility
ccor <- pmin(1, cor+(cor-predict(md, s1)))

plot(idx, cor, type="l", ylim=c(-1, 1))
lines(idx, ccor, col="blue")
lines(idx, predict(loess(ccor~idx)), col="green")

From my point of view, the only way to find true diversification is
investing in different sectors such as bonds or real estate or investing
in different strategies, e.g., hedge funds being long volatility (but
also in these examples correlations increased in the past few years, and
it is difficult to find true diversification).

Best

>Message: 12
>Date: Wed, 22 Aug 2007 10:34:59 +0200
>From: "Sylvain BARTHELEMY" <barth at tac-financial.com>
>Subject: Re: [R-SIG-Finance] making sense of 100's of funds
>To: "'R-sig-finance'" <r-sig-finance at stat.math.ethz.ch>
>Message-ID: <006901c7e497\$542c1c00\$fc845400\$@com>
>Content-Type: text/plain;	charset="iso-8859-1"
>
>
>
>
>>>>> I fully agree with you....the myth of diversification is great for
>>>>> academic purposes.  We run a portfolio of hedge funds and try to look at
>>>>> correlations of our managers in a portfolio...but the pattern you
>>>>> describe below is exactly what we see...detract from performance in an
>>>>> up market and as correlations go to 1, don't offer enough protection in
>>>>> a down market.  The only time it may work is a nontrending market, in
>>>>> which case it may be better to have a diversified portfolio?
>>>
>>>
>
>Yes, I agree with the fact that it does not offer enough protection, but it
>offers some, even if portfolio managers expect more.
>
>You were talking about recent events. So, imagine what would be the impact
>of the US sub-prime crisis in Europe if the banks and funds were less
>diversified. The liquidity problem could become a solvency problem and a
>crash much more rapidly than it does.
>
>Diversification is like an airbag, and the only thing you know is that if
>you have SP500 portfolio, in case of crisis, you may lose less money than
>unlucky managers but maybe more than lucky ones. The rest is a matter of
>price. What is the price/return that you would put on that?
>
>Managers usually expect too much about the benefits of diversification and
>would like high returns without any risk... but unfortunately, it is not
>possible! Today, the price of diversification is high but it offers more
>stable return even if it this protection low in case of crashes.
>
>Finally, the horizon and objectives of practitioners matters. Then, the
>diversification benefits are very different from the point of view of the
>portfolio manager of an hedge fund, a international bank (doing retail of
>investment banking) or the CEO of a multinational company.
>
>
>
>
>>>>> The problem is that the reversals are so rapid that is may well be
>>>
>>>
>
>I fully agree with that.
>
>
>
>
>>>>> My point is that in today's markets diversification dumbs down a
>>>>> portfolio during expansions--I'll grant that in some cases that there
>>>>> may be some pickup in risk-adjusted returns. However, when it comes to
>>>>> decline such as the one we just saw, diversification offers cold
>>>>> comfort to the practitioner as correlations converge. Unfortunately it
>>>>> is exactly in these times that the benefits of diversification are
>>>>> most counted on and most missed.
>>>
>>>
>
>Again, I fully agree with that but my answer is not that diversification is
>a myth: there is a big difference between "cold comfort" and "no comfort".
>
>
>
>
>>>>> Hell, there are no rules here, we are trying to make money.
>>>
>>>
>
>"In theory, there is no difference between theory and practice. But, in
>practice, there is"
>
>
>---
>Sylvain Barth?l?my
>Research Director, TAC
>www.tac-financial.com | www.sylbarth.com
>
>
>-----Message d'origine-----
>De?: r-sig-finance-bounces at stat.math.ethz.ch
>[mailto:r-sig-finance-bounces at stat.math.ethz.ch] De la part de BBands
>Envoy??: mardi 21 ao?t 2007 21:47
>??: R-sig-finance
>Objet?: Re: [R-SIG-Finance] making sense of 100's of funds
>
>On 8/21/07, Sylvain BARTHELEMY <barth at tac-financial.com> wrote:
>
>
>>> John,
>>>
>>>
>>
>>
>>>>> >> The benefits of diversification are a myth, or, more properly, a
>>>>> >> nightmare. (They did exist once upon a time, but that was long, long
>>>>> >> ago.)
>>>>
>>>>
>>>
>>> No, I don't agree with that. The benefits of diversification are not easy
>>
>>
>to
>
>
>>> quantify and maybe less important than in the past, but I would not say
>>
>>
>that
>
>
>>> it is a myth or even a nightmare.
>>>
>>> It is true that financial markets are more and more integrated and that
>>> contagion is usually observed during financial crises, especially on
>>> emerging markets. But the impact of large events and crises are less
>>> important on well diversified portfolio (geographically, different
>>> instruments, different sectors,...).
>>
>>
>
>In practice that doesn't seem to be the case. In this cycle in
>particular most things were sold off with a maddening similarity. The
>following was sent to me off list:
>
>"""
>I fully agree with you....the myth of diversification is great for
>academic purposes.  We run a portfolio of hedge funds and try to look at
>correlations of our managers in a portfolio...but the pattern you
>describe below is exactly what we see...detract from performance in an
>up market and as correlations go to 1, don't offer enough protection in
>a down market.  The only time it may work is a nontrending market, in
>which case it may be better to have a diversified portfolio?
>"""
>
>
>
>>> I don't think that diversification disappear, but that the way to
>>
>>
>construct
>
>
>>> a diversified portfolio changes over time, as financial markets change.
>>
>>
>
>The problem is that the reversals are so rapid that is may well be
>
>
>
>>>>> >> In today's markets on the way up diversification averages down
>>>>> >> returns, while on the way down diversification offers no benefits as
>>>>> >> correlations converge on one.
>>>>
>>>>
>>>
>>> Yes, maybe the correlation should converge on one as financial markets are
>>> more and more integrated.
>>>
>>> But the fact is that correlation measures usually show very unstable
>>> process, and they can changes very rapidly from uncorrelated one to high
>>> correlated markets, especially during crises (see correlations between
>>> emerging markets during the 97 crisis). Then, all this is very different
>>> from a smooth trend toward less diversification gains and more correlation
>>> between world markets.
>>
>>
>
>My point is that in today's markets diversification dumbs down a
>portfolio during expansions--I'll grant that in some cases that there
>may be some pickup in risk-adjusted returns. However, when it comes to
>decline such as the one we just saw, diversification offers cold
>comfort to the practitioner as correlations converge. Unfortunately it
>is exactly in these times that the benefits of diversification are
>most counted on and most missed.
>
>
>
>>>>> >> Having said that, I'll crawl into my bunker and await the incoming.
>>>>
>>>>
>>>
>>> Don't crawl into your bunker, it is an interesting topic, and not only for
>>> banks and portfolio managers. I would be interested to know more about
>>
>>
>your
>
>
>>> ideas on that.
>>
>>
>
>I've found that when tackling shibboleths, a bunker offers some comfort.
>
>To paraphrase one of Dirk's signatures.
>
>Hell, there are no rules here, we are trying to make money.
>
>    jab
> -- John Bollinger, CFA, CMT www.BollingerBands.com If you advance far
> enough, you arrive at the beginning.
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