Bubblesofearth wrote:hiriskpaul wrote:
Good, so we are in agreement then that "The drawback with unequal weights on purchase .. is the likelihood of reduced returns" is not true?
If you agree there is a 2/3 chance of under-performance with extreme overweighting in the previous 3-share example then how does that not correspond to a likelihood of reduced returns?
I thought we had already covered that and you were in agreement! Clearly not, so I will give an illustration. This is not intuitive, so I don't blame anyone for questioning it.
Take 3 stocks A, B and C. After a certain period of time the prices will have changed by factors a, b and c respectively. If you invest with weights Wa, Wb and Wc, where Wa+Wb+Wc=1, then for each pound invested, you will end up with a*Wa+b*Wb+c*Wc. Now lets say A halves in price (a=0.5), B goes up by 50% (b=1.5) and C goes up 300% (c=4), so 2 stocks underperform the average, 1 outperforms, but you have no in advance knowledge of the differences in performance that would give you an edge. What is the optimal weighting (ignoring risk)? The answer is that weighting does not matter.
Lets say you put equal amounts into all 3 stocks. The the return will simply be the arithmetic average return (0.5+1.5+4)/3 = 2. You get £2 back for every £1 invested. Now consider what happens if you pick just one stock. You could have picked A, B, or C and you have no edge, so each pick is equally likely. Expected return is then 0.5/3 (you picked A) + 1.5/3 (you picked B) + 4/3 (you picked C). Net result 2 again. If you picked 2 stocks with equal weight, then you must either have picked (a,b), (a,c) or (c,a). Again equal 1/3 likelihood of each portfolio. The return if you had picked (a,b) is a*Wa+b*Wb = (0.5*0.5+1.5*0.5) = 1. Similarly, the return for (a,c) is (0.5*0.5+4*0.5) = 2.25 and the return for (b,c) is (1.5*0.5+4*0.5) = 2.75. Expected return is then 1/3+2.25/3+2.75/3 = 2 again.
Trying something more complicated weights of (0.2, 0.3, 0.5). With no edge, there are 6 equally likely portfolios that could have been formed with these weights (a,b,c), (a,c,b), (b,a,c), (b,c,a), (c,a,b), (c,b,a). The return from portfolio (a,b,c) is (0.5*0.2+1.5*0.3+4*0.5) = 2.55. Similarly for the others, the returns are in order 2.05, 2.45, 1.75, 1.7 and 1.5. The expected return is than simply the average of the equally likely portfolios, which comes out at 2. Whatever weights you assign to A, B and C, even negative ones indicating you have gone short, the expected return will always be 2 (provided the sum of the weights is 1). It is not hard to mathematically prove that the expected return on a portfolio of stocks is independent of the underlying distribution of returns and independent of stock weights.
When risk is brought in, you could optimise for minimum volatility, but if that is your aim by going for equal weight it will not work. Equal weight would match minimum volatility if all stocks had the same expected returns, volatilities and correlations. In the real world an equal weight portfolio can end up more volatile than the equivalent cap weighted index (you can see it with the S&P, S&P equal weighted indices). An equally weighted portfolio is just a stab in the dark and no better than cap weighted. It will not have a higher expected return, aside from small cap factor, and will require a lot more maintenance to keep in balance.
OK, it appears I'm out of date with my understanding of the relative volatilities of RDS and RB (I'm sure they were roughly the same not that long ago). But from what you've pointed out it would appear that RDS is actually riskier than RB based on volatility. As for believing potential rewards from RDS are higher than for RB that flies in the face of the share price performance over the last couple of decades where RB has utterly trounced RDS. Far from plodding along shares in RB have gone up some 15X from their low in 1999! Not a predictor of future performance but does make believing RDS is likely to provide higher rewards hard to swallow.
So you know better than the market then, based on what has happened in the past? If you are convinced you do (lots of people are) then why bother to equal weight? Optimise your portfolio based on your own convictions on risk/reward. It is very important for us tracker buyers that there are sufficient investors prepared to do that.
But my point is not that RB is a better bet than RDS. It is that there is no rationale, based on risk/reward, for an individual allocating 4X as much money to RDS even though that is what the market as a whole does. And it is exactly what you are doing when you buy your Globally diversified portfolio of trackers. Just because you are comfortable with the weights in your equity portfolio does not mean they represent an optimal allocation.
There is no rationale, based on risk/reward, for buying them equally weighted.
You can't assess risk by just selecting one years performance.
Agreed. And you cannot assess a portfolio building strategy based on a single empirical sample with no rational explanation as to how these excess returns were achieved.
Can you point to a single study that shows long-term outperformance of a cap-weighted index vs an equal weight LTBH portfolio of shares taken from that index?
No, neither can I point to a study on myriad other wacky/irrational ideas for portfolios that someone might dream up. Not any that stand up to scrutiny anyway. I can point to an equally weighted S&P 500 ETF that has beaten the S&P 500 since it was launched though - Guggenheim's RSP. It is more volatile than the S&P, dropping more in down turns and rising faster in rising markets. More trading is required to keep the ETF in balance than with a cap weighted ETF like SPY, but that has clearly not detracted too much from performance. However, smaller caps have tended to outperform larger caps since RSP was launched. If the small cap factor turns negative for a prolonged period, RSP might underperform the S&P.
Someone on the old TMF boards (LookingForClues) chose to buy a broad portfolio of stocks, equally weighted and then simply leave them to do their own thing. I have thought about that and discussed it a few times. In the end think I concluded that there was nothing particularly wrong with his approach, in fact in some ways I quite like it. The only clear downside was that the portfolio will be likely to get increasingly unbalanced/less diversified over time and specific risk will rise. Provided the portfolio was broad enough though it could take many years (longer than LFC's expected holding period) before specific risk became a significant problem.
The only (rational) reasons I can think of as to why such a portfolio might beat a cap weighted tracker are 1) random chance, 2) overweighting of smaller caps, 3) Potentially lower ongoing charges than the tracker. Ignoring 2 and 3, I can see little reason to say the portfolio should not have a 50/50 chance of beating the cap weighted tracker. With 2 and 3 as well, I reckon he has better than even odds. The only other thing that occurred to me that could be a problem is that he is getting less new blood into the portfolio compared to a tracker. This can come from takeovers, or other corporate actions when he gets cash to reinvest elsewhere. A tracker will as well buy into new companies when they enter the index. I have no evidence to suggest this might drag performance, it is just a nagging doubt.
Are you simply happy to accept the word of those who say you can't beat the (presumably cap-weighted) market? Do they have an agenda (ref you comment on the agenda of those presenting the Dow study)?
It depends what you mean. It is factually and logically incorrect to simply say "you can't beat the (cap-weighted) market". Generate a few thousand portfolios with weights randomly distributed about cap weights and I would expect half of those portfolios to beat the market. Generally though I think what people mean is that high charging/high turnover fund managers cannot beat the market over prolonged periods. Or more precisely, the percentage of high charging managers that beat the market will diminish over time. There is plenty of evidence to support that hypotheses, with more being produced every year. If active fund managers charged the same as cap weighted trackers and nothing for trading, the active managers would on aggregate perform the same as cap weighted trackers.
As to whether someone saying "you can't beat the market having an agenda", then yes of course some will.