Correlation and volatility reduction

[IndependentlyPoor]

I must admit that I hate the way the stock market grants moral absolution to all of us who profit from companies that do things the we would consider immoral, but I don't have any idea at all of what to do about it, other than what Ziggy said.

I also hate to spoil this interesting series of posts with another Geek bomb, but folks asked about consistent time periods and three fund portfolios, so I ran some.

I optimized three fund portfolios for maximum return/volatility. (Not the same as maximizing for minimum volatility.) Each portfolio consisted of one fund from Vanguard's general stock category, one from the international/aggressive/sector categories, and one bond fund.

Again, with 20/20 hindsight, the optimizer pretty much eliminated the general stock funds from the portfolios. It seems like barbell portfolios with sector funds and treasuries was where to be since 1991.

The chart also shows the risk/return of Vanguard's balanced funds for comparison, but I did not include the balanced funds in any portfolios. Likewise, the chart shows the risk/return of the individual funds that make up the portfolios.

Here is a screenshot of the interactive graphic.


When you hover the cursor over a point, it shows the fund name(s) and allocations for the portfolios. Here, the popup is showing Wellesley.

The three fund portfolios are in red (although the general stock fund allocation was optimized to zero in many),
the balanced funds in blue,
and the individual funds that make up the portfolios in purple.

One thing that jumps right out at you is that the individual funds have much more volatility than the portfolios, so something is working.

You Wellesley fans should be happy to see that it does well in this comparison.

You need the free Mathematica Player for the interactive graphic.
It is here:
Wolfram Mathematica Player: Download
And here is the link to the interactive graphic:
http://www.wolfram.com/solutions/in...441069&filename=Three+fund+portfolios+pub.nbp

 

[Gumby]

I have a co-worker who's a Muslim, and that religion forbids loaning money at interest. The pension fund has lots of bonds in its holdings. That's a real dilemma for him.

There are some very new mutual funds that invest in sukuk instead of traditional bonds:

European Finance House launches sukuk fund, Qatar Debt, Markets - Maktoob Business

International Adviser :: HSBC targets Gulf investors with first sukuk fund

When you say "pension fund", do you mean defined benefit or defined contribution? If it is a DC plan, there may be a self-directed option that would allow your co-worker the use of a sukuk fund.

 

[Animorph]

Don't forget you need to rebalance periodically in order to really benefit from this. If all you do is buy and hold, you'll just get the averaged return for the funds and volitility will hardly matter (at least in terms of the numbers you are looking at). Rebalancing is supposed to be worth about 1% annually, on top of just buying and holding the funds.

Ideally each component would have roughly the same return but negative correlations. If the returns are not comparable, the final return of the portfolio will be lowered. If you could pair two negatively correlated equity funds instead of an equity fund and a cash fund, that should provide better total returns, at least in theory.

With rebalancing, you actually want as much volitility as you can get for each individual fund. Then when one is way up or down you can balance it out with the others. The more movement, the more benefit from rebalancing.

 

[kyounge1956]

There are some very new mutual funds that invest in sukuk instead of traditional bonds:

European Finance House launches sukuk fund, Qatar Debt, Markets - Maktoob Business

International Adviser :: HSBC targets Gulf investors with first sukuk fund

When you say "pension fund", do you mean defined benefit or defined contribution? If it is a DC plan, there may be a self-directed option that would allow your co-worker the use of a sukuk fund.

It's a defined benefit plan. I don't know if the prohibition includes interest received by another party on your behalf, or only to interest received by you personally. If the former, then the DB plan is no problem; if the latter he really is in a bind, because I don't think there is any way for employees to opt out of the pension plan even if they want to.

There is also a DC plan, and it does have a self-directed option, but this has restrictions and extra fees. He's pretty young, so he could allocate his DC contributions (if any) 100% to equities, buy permissible non-equity investments in an IRA or brokerage account, and avoid those extra costs. The topic just came up briefly in passing, so I don't know what he has decided to do.

 

[John Galt]

I vacillate between wanting to be an index investor (for all the usual reasons) and wanting to invest in individual stocks (to be more socially responsible).

What do you mean by more socially responsible?

In a classic piece in Journal of Finance in 1968, Evans and Archer found that portfolios with as few as 10 securities had risk, measured as standard deviation, virtually identical to that of the market.

Jim Cramer does a segment on Mad Money called 'Am I Diversified' where people send in there 5-stock portfolios and he tells them whether they're diversified across different sectors. So maybe even 5 stocks is enough?

 

[IndependentlyPoor]

Minimum volatility three-fund portfolios

Here are the same three fund portfolios as before, except this time they are optimized for minimum volatility rather than maximum return/volatility.

The portfolios include one fund from Vanguard's general stock category, one from their international/sector/aggressive category, and one from their bond category. I only included funds for which I could get data over the full time range of 1/1/1992 to the present.

The 3 fund portfolios are in red, and the individual funds that comprise them are in purple. I included some balanced funds in blue for comparison. Wellesley fans will be pleased to see that VWINX holds up well here.

The best way to peruse this is to download the Mathematica Player from here
Wolfram Mathematica Player: Download
and the interactive graphic from here.
http://www.wolfram.com/solutions/in...979464939&filename=Three+fund+min+vol+pub.nbp
If you hover the cursor over a point, the popup displays the portfolio allocation (or fund name) along with the APR/Std.Dev. ratio.

Here is a screen shot of what the interactive graphic looks like.


It seems clear that the portfolios generally have much lower volatility than the individual stock funds. Bonds seem to have been the place to be: the Total Bond Market Fund and (surprising to me) the High-Yield Corp. Fund show very attractive return/risk characteristics. Vanguard's balanced funds (Wellesley, Star, and Wellington) look mighty good.

 

[kyounge1956]

I vacillate between wanting to be an index investor (for all the usual reasons) and wanting to invest in individual stocks (to be more socially responsible).

What do you mean by more socially responsible?

In an nutshell, I mean not profiting from doing bad things, and/or investing in a way that promotes good things. Some people also include shareholder activism in their definition of socially responsible investing. I don't know if I would get involved in that end of it. I'm reading a book at the moment called Slow Money and there was also a thread here at ER a few months ago on Financial Permaculture. I think both of those, which are efforts toward promoting sustainable local food production and keeping money circulating in local economies (rather than sending it out of town to national or larger companies) could also be included under the umbrella of socially responsible investing.

 

[samclem]

Jim Cramer does a segment on Mad Money called 'Am I Diversified' where people send in there 5-stock portfolios and he tells them whether they're diversified across different sectors. So maybe even 5 stocks is enough?

Absolutely not.

 

[kyounge1956]

It is more stocks than most people realize. Here's what William Bernstein said:

One of the most dangerous investment chestnuts is the idea that you can successfully diversify your portfolio with a relatively small number of stocks, the magic number usually being about 15. For example, Ben Graham, in The Intelligent Investor, suggests that adequate diversification can be obtained with 10 to 30 names. In a classic piece in Journal of Finance in 1968, Evans and Archer found that portfolios with as few as 10 securities had risk, measured as standard deviation, virtually identical to that of the market. Over the decades, the "15-stock diversification solution" has become enshrined in various texts and monographs . .
. . .
[in recent years] a grossly disproportionate fraction of the total return came from a very few "superstocks" like Dell Computer, which increased in value over 550 times. If you didn’t have one of the half-dozen or so of these in your portfolio, then you badly lagged the market. (The odds of owing one of the 10 superstocks are approximately one in six.) Of course, by owning only 15 stocks you also increase your chances of becoming fabulously rich. But unfortunately, in investing, it is all too often true that the same things that maximize your chances of getting rich also maximize your chances of getting poor.
If the O’Neal data are generalizable to stocks, and I believe that they are, then even 100 stocks are not nearly enough to eliminate this very important source of financial risk.

It looks like a catch 22. If I understand this, fifteen or twenty stocks might have the same standard deviation as the total market, but lower return, so in order to keep the same return in my portfolio the overall equity allocation would have to be higher than if I used a total stock market fund, which would increase the standard deviation of the portfolio as a whole.

I have also wondered if it would be possible to avoid certain income sources by use of sector funds. For example, maybe I could eliminate tobacco profits from my income sources by splitting my equity allocation between all of some fund family's sector ETFs except Consumer Staples. That would eiminate tobacco profits, while retaining an exposure to most of the stock market, but with the low expenses of indexed investments. It wouldn't be possible to screen for some sort of corporate practice one found objectionable in this way, because it probably wouldn't be confined to a single sector, but to eliminate profits from a few specific sources, maybe it would work, unless the tobacco companies are among those "superstocks".

 

[IndependentlyPoor]

How many individual stocks are required to create a diversified portfolio is (IMHO) an interesting question, so I geeked out on it. I picked a universe 14 well-known stocks and then formed all possible 2, 3, 4, and 5 stock portfolios from this 14 stock set: 3472 portfolios all together. Then I optimized the allocations in each portfolio for minimum volatility. The time span was from 1988 to the present. The stocks were
AAPL, DELL, F, WFC, T, MO, GE, BA, XOM, AET, ADM, DD, CAT, PFE

The chart below shows the risk/return for these minimum volatility portfolios.
black points - single stocks
red points - two-stock portfolios
yellow points - three stock portfolios
green points - four stock portfolios
dark blue/green points - five stock portfolios
big blue point - VTSMX

You can see the trends in this plot, but that is about it. Note that many portfolios have less volatility than VTSMX, but at lower return.

Here are some averages of the portfolio performance for each group.

Num. Stocks	Mean Std.Dev.	Mean Return	Mean Return/Std.Dev.
5	1.31	1.36	1.06
4	1.37	1.3	0.97
3	1.47	1.25	0.87
2	1.66	1.24	0.76
1	2.19	1.5	0.64

The Mean Return/Std.Dev. increases almost linearly with the number of stocks! Here is a plot of the same data.
red - Mean Std.Dev.
green - Mean Return
blue - Mean Return/Std.Dev.


And here are the minimum volatility portfolios for each group

I can post the interactive Mathematica chart if anybody is interested. It shows the portfolio allocations for each point in a popup.

 

[samclem]

It looks like a catch 22. If I understand this, fifteen or twenty stocks might have the same standard deviation as the total market, but lower return . . .

Or, the 15 stocks might have much higher returns. According to what Bernstein found, the overall return from the few "superstocks" was so significant in moving the overall average of the index that going with a smaller sample significantly increased the standard deviation (both ways). He shows that the importance of "superstocks" was much more important in driving the magnitude of changes in the overall market indexes than was the case in the 1950s and 1960s, which is why the old "15 stocks is enough" idea was no longer a valid one.

 

[kyounge1956]

Or, the 15 stocks might have much higher returns. According to what Bernstein found, the overall return from the few "superstocks" was so significant in moving the overall average of the index that going with a smaller sample significantly increased the standard deviation (both ways). He shows that the importance of "superstocks" was much more important in driving the magnitude of changes in the overall market indexes than was the case in the 1950s and 1960s, which is why the old "15 stocks is enough" idea was no longer a valid one.

So the basket of fifteen stocks will have both lower return and lower volatility than the total stock market, unless it includes one or more superstocks, in which case it will have much higher return but also much higher volatility? Have I got it right yet?

This leads me to pose all sorts of questions:

• what "recent years" comprise the period in which the superstocks had this disproportionate effect?
• were the same stocks "super" throughout that time period?
• Are those stocks still "super"?
• Are we still in the "superstock" era, or have conditions settled back down to be more similar to what they were when the "15 stocks is enough" idea was first developed?
• Does "lower return" mean lower than overall historic stock market, or only lower than the period when the superstocks were showing explosive growth?

and so on...

 

[samclem]

So the basket of fifteen stocks will have both lower return and lower volatility than the total stock market, unless it includes one or more superstocks, in which case it will have much higher return but also much higher volatility? Have I got it right yet?

Yes, or at least that's how I interpret what he wrote.

This leads me to pose all sorts of questions:

• what "recent years" comprise the period in which the superstocks had this disproportionate effect?
• were the same stocks "super" throughout that time period?
• Are those stocks still "super"?
• Are we still in the "superstock" era, or have conditions settled back down to be more similar to what they were when the "15 stocks is enough" idea was first developed?
• Does "lower return" mean lower than overall historic stock market, or only lower than the period when the superstocks were showing explosive growth?

I dunno, but these questions lead us into predictions of the future (both for the whole market and individual securities), which I think Bernstein would warn against. It's fair to say that "superstocks" would probably be more likely to emerge and grow in an environment that favors growth stock (over value stocks). But, if we could predict that, we'd all be rich from buying options and shorting appropriate indexes.