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Learning outcomes.

Â After watching this video you will be able to,

Â one, understand style analysis and how it is carried out.

Â Now we move on to something called style analysis,

Â which is very interesting.

Â Introduced for the first time by Professor William Sharpe who also by

Â the way won the Nobel Prize for coming up with the capital asset pricing model.

Â Now, the style analysis model is very popular in the practitioner world.

Â The basic idea here is to say,

Â now how much of the variation of my particular fund can be explained

Â simply as a combination of a bunch of passive index investments.

Â To be more formal,

Â suppose I have a bunch of indices on the right hand side

Â represented in this equation by F_1 through F_n.

Â What I want to do is,

Â I want to fit an equation r_p = [b_1 F_1 + b_2 F_2 +... + b_n F_n]+ e_p.

Â It looks like a regression equation,

Â but this is not really a regression equation.

Â The difference is number one,

Â here Sharpe wants to constrain the betas to all lie between zero and one,

Â and he wants the sum of the bs to be constrained to one.

Â In other words, he's thinking of the bs really as portfolio weights.

Â The idea is to the extent possible,

Â can we figure out a set of weights which could have been employed by

Â a passive investor to largely mimic the variation in returns of this fund?

Â Of course, you're never going to do a perfect job of mimicking

Â the fund using a combination of these indices on the right hand side.

Â The idea is to find the best possible combination exposed,

Â that is, after the fact.

Â The way to do this is to essentially minimize

Â the variance of that error term and figure out

Â the right combination of the bs that would have minimized the variance of the

Â e. And the idea is there's an R-squared type measure here,

Â which basically says most of the variation on

Â this active managed fund could have been essentially

Â replicated by a certain combination of index funds on the right hand side,

Â then the active fund manager is not doing much.

Â If there is a significant part of the variation which cannot be

Â explained by a combination of passive investments in the right hand side,

Â then we begin to give some credit to the active fund manager.

Â Now this style analysis is a,

Â easy, b, interesting, and c, very very useful.

Â Now it can be used in a variety of ways and I'm going to show you

Â an example very soon as to how it can be used.

Â In particular, it can be used very easily to check if funds

Â follow the philosophy they say they will follow.

Â For example, today in the United States as well as in several countries,

Â lot of funds essentially align themselves along something called a style grid.

Â On one axis, you have say growth and value as the polar opposites.

Â On another axis, you have size that is small to large as the polar opposites.

Â Obviously, you can have,

Â let's say nine quadrants on that three by three,

Â and basically say, "Well,

Â I'm a large cap value fund.

Â I'm a small cap growth fund etc."

Â Now it is all well for a fund to say that they follow a certain philosophy,

Â but it is up to you, the investor, or up to you,

Â the analyst, to actually figure out if the fund is actually

Â following the particular style that they're saying that they will follow.

Â Now, here what I've done is essentially I've taken a couple of U. S. stock mutual funds.

Â These are large mutual funds,

Â one of them is 32 billion in size,

Â the other is about half that size,

Â about 16 billion, still very large.

Â One is the Vanguard fund,

Â other one is the Fidelity Dividend Growth fund.

Â Now the interesting thing is,

Â the Vanguard fund advertises itself,

Â I plucked this off their website,

Â they say they are a large growth fund.

Â The Fidelity fund on the other hand says they're a large blend fund,

Â blend being, they're a blend of growth and value.

Â And Morningstar, which is a well-known mutual funds rating agency,

Â happens to give the Vanguard fund

Â a five star rating and the Fidelity fund a three star rating.

Â Now my quest is very simple.

Â I want to look at the battery of measures we've all

Â studied until now and see if we can employ

Â some of those measures and come up with

Â a measure that replicates what Morningstar is doing.

Â In other words, are our measures doing what they're supposed to do?

Â Do they lead to the same conclusions as the Morningstar ratings?

Â I have a bunch of data which is slightly dated now but it will serve the purpose.

Â My data goes from January '94 all the way through November 2005,

Â which is about 143 months of data.

Â I'm going to use all our performance measures,

Â and if you sit down and collect the returns of

Â these funds and calculate each of these measures that we have discussed,

Â what you've seen in the table is that really, yes,

Â there is some slight edge of the VP fund,

Â which is the Vanguard fund,

Â over the Fidelity fund in terms of slight increase

Â in Sharpe ratio or slight increase in say,

Â the one factor alpha etc.

Â But nothing really pops out at you from this table.

Â In other words, it's practically impossible to conclude just

Â from this set of numbers that somehow we

Â have this superlative performance of

Â the Vanguard fund as opposed to the mediocre performance of the Fidelity fund.

Â I try to use style analysis now,

Â and since these are both equity funds,

Â I use as my passive indices or styles as Sharpe calls them,

Â on the right hand side,

Â I use six particular styles.

Â The first one is a large cap growth index,

Â which is essentially within the S&P 500,

Â all the high market to book stocks.

Â Market value to book value stocks.

Â And the large cap value,

Â I have essentially that half of the S&P 500 which is the low market to book,

Â or conversely the high book to market stocks.

Â Similarly, mid-cap growth mid-cap value,

Â small cap growth and small cap value.

Â Essentially, I have six indices on the right hand side as regress source if you will,

Â in the Sharpe style analysis.

Â Now what I have on the right hand side in the graph is that,

Â I have derived the optimal bs if you will,

Â the optimal rates, that could have

Â largely replicated the variance in fund returns for both funds.

Â First, the Vanguard fund,

Â and the Vanguard fund it turns out has exposure to large growth,

Â to small growth, to mid-cap growth, and large value.

Â And what did they say they were?

Â They said they were a large cap value fund.

Â Sorry, they said there were a large growth fund.

Â With style analysis, what we look at with

Â the Vanguard fund and the Fidelity fund is that the weighting

Â of different passive benchmarks that could have potentially

Â replicated the performance of these two funds is shown in these two graphs.

Â Now with the Vanguard fund,

Â what we see is it has exposures,

Â not just a large growth as it purports to be,

Â but also to other things like large values,

Â small growth, mid-cap growth, etc.

Â However, with the Fidelity fund,

Â which says it is a large blend fund,

Â you will see that the largest exposures are to large value and large growth.

Â In other words, if you pardon me the pun,

Â the Fidelity fund shows greater fidelity to

Â its investment objective rather than the Vanguard fund.

Â The other thing we could do is to actually

Â conduct a rolling style analysis, that is to say,

Â we take x number of months of returns and roll

Â the window across which you determine

Â the style of the fund up to the very end of the data,

Â and you see how a fund style has evolved across time.

Â And what you see of course is that in the Vanguard case,

Â the style has been changing a lot over time.

Â More importantly, it has never really been an exposure only to large growth,

Â it has been exposed to several other styles if you will over time whereas,

Â with the Fidelity blend fund,

Â what you see is, although it had exposures to other kinds of styles in

Â the beginning of the sample period towards the latter part of the period,

Â the exposure is almost exclusively large growth and large value as it should be.

Â Now we could potentially use this style exposure at every point,

Â because we have a style exposure at every month,

Â beyond a certain month,

Â until the end of the period as the appropriate benchmark for this particular fund,

Â and try to benchmark the fund to its own style benchmark.

Â In other words, we are now benchmarking both these funds not

Â against S&P or any other such index but we are saying,

Â I have my own special weighted set of

Â passive benchmarks that I'm going to call the benchmark for VPMCX and I have my,

Â again, similar set of a style benchmark for

Â FDGFX and I'm going to benchmark the fund performance against its own style benchmark.

Â And when you do that,

Â some things start to pop out right there.

Â And what you see is,

Â if you look at the Vanguard fund against its style benchmark,

Â for the first time, statistically, significantly,

Â there is an out-performance relative to its style benchmark.

Â In fact you can do this more formally and try to run a regression

Â of each of these fund returns against the S&P,

Â against the Fama and French three-factors,

Â which is the market factor,

Â the small minus big factor,

Â and the high minus low factor as you know, and of course,

Â now the new addition,

Â the last row of this table,

Â which is the rolling style benchmark.

Â And what you see is,

Â results are practically statistically

Â insignificant in the S&P case and the Fama-French three-factor case.

Â But when you look at the rolling style analysis,

Â what you see is of course,

Â that the Vanguard fund has an out-performance of 1% per month as

Â opposed to the Fidelity fund of 0.61% per month.

Â And the performance is much more statistically significant with the Vanguard fund.

Â It is of course, also significant with the Fidelity fund,

Â which earned it three stars if you remember,

Â with the Morningstar guys,

Â but clearly Vanguard emerges as the outperformer among the two.

Â And now you see why Morningstar would actually give the

Â former fund a five star rating and the second fund a three star rating.

Â That is the clear use of style analysis which I said is a very interesting analysis.

Â