October 12, 2017

A Price Tag on Alpha - Part III of III

This 3-part series: A Price Tag on Alpha is trying to answer the question: What would people pay for performance of over 25% on a yearly basis? Part I covered the basics and Part II left some questions unanswered especially concerning the price one should pay for this 15% alpha.

A 15% alpha starts to be interesting if, and, I would say only if, F0 (the initial capital) is large enough, and that the trading strategy is designed to maintain its CAGR for years. If not, the strategy is not worth as much.

Almost anybody can backtest a short-term stock trading strategy and produce a 25% CAGR. Nonetheless, if put out live, it could still underperform averages, especially if the strategy was over-fitted. But, that is not the question being asked.

To me, one needs to show that his/her stock trading strategy can maintain its 25% CAGR for at least 10+ years on a large portfolio. And that the CAGR does not degrade as the size of the portfolio grows. Even then, it will turn out to be a question of trust, of the narrative, the operational structure and the worthiness of the underlying premises. It will need to all make sense.

Exchanging Alpha For Capital

One could opt to substitute alpha points for capital right from the start.

The following equality holds: F0∙(1+ rm )t = λ∙F0∙(1+ rm + α)t, where λ will scale F0 to produce the same outcome using less capital with: λ = (1+ rm )t / (1+ rm + α)t. This exchange seems attractive, and it depends entirely on our ability to generate the alpha. A zero alpha gives a lambda of one: λ = 1, the average market return scenario (see Part I and Part II).

A $77,563 fund at a 25% CAGR will produce the same outcome as a $1 million dollar fund at a 10% CAGR over the same 20-year time interval.

If you can get the 15% alpha, you could produce the same amount of profits with only 7.756% of the initial $1M dollar fund. So, is the alpha valuable? Again, yes.

Regardless, I see it still as a total waste. This alpha generator, by not going for the $1M fund, and maintaining its 15% alpha edge, is relinquishing an $86.7M outcome. Evidently, the other outcome amounts to only 7.756% of what he/she could have done with the added capital. This is a high opportunity cost. If you have the alpha, then go for it all the way, find the capital.

If you add a zero to this scenario and make it a $10M dollar fund, then the 10% CAGR would produce over 20 years: $ 10M∙(1+ 0.10)20 = $ 67,274,999. Compare this with the added 15% alpha which would have generated the same amount but would have required only $775,627. Here is the calculation: $775,627∙(1+ 0.10 + 0.15)20 = $ 67,274,999.

This is where the waste of some good alpha comes in: $10M∙(1+ 0.10 + 0.15)20 = $867,361,738. Because someone could not or did not want to do the extra work of getting more capital, they were throwing away some $800,086,742! This, not because of the trading strategy, but because they failed to raise their initial stake.

Evidently, this is on the premise that the alpha was there in the first place, and was sustainable for the period. If your stock trading strategy is not scalable to that level, or can not last that long, then what do you think it is worth?

Should you add 10 years to the above scenario, you would get: $10M∙(1+ 0.10 + 0.15)30 = $8,077,935,669. Now, that 15% alpha has to be considered a game changer.

The conclusion would be: if you can get the alpha, meaning a sustainable alpha, and on a scalable trading strategy, then this alpha is worth a lot more to you than to anybody else. But, it would appear as if it does not bother anyone to almost give it away. Why is that?

My advice would be: don't sell yourself short. Do the extra work. And, as a minimum, get a reasonable piece of the pie.

If you do not plan for these things, how do you think you will get them?

So, how much is a sustainable and scalable 15% alpha worth? It could be quite a lot since this alpha is part of the compounding.

Back To The Question

Still, have not answered the initial question. Maybe a look at the spreadsheet used for the previously presented charts could be of help.

 #5  20-Year CAGR and Fees
20-year CAGR and fees

(click to enlarge)

Of interest is column (6) where the charges are represented as a fraction of total portfolio profits. According to the numbers, at the 20-year level, the accumulated charges represent about 38.93% of profits which will go to the hedge fund manager(s).

The picture is more compelling when looking at the 30-year level. There, 51.81% of all profits will have gone to pay the 2/20 hedge fund fees (see figure #6).

 #6  30-Year CAGR and Fees
30-year CAGR and fees

(click to enlarge)

Could I say that if over time more than half of all generated profits will go to the fund manager, then he or she is more than reasonably compensated.

Notice that I did not include the 2% annual management fee in those calculations. It would have increased the portfolio manager's take even more.

In fact, if you add the 2% fee to figure #6, the drag on the generated profits for the 20-year scenario would go from 38.93% to 69.22%. Meaning that almost 70% of all the profits the trading strategy could generate would go to the hedge fund, not you.

The picture is more dramatic if you look at the 30-year interval. From figure #6, the drag on profits was 51.81%, now it jumps to 82.35%!

So, it is not 22% for them, and 78% for you. It is 82% for them and 18% for you.

In the beginning, the 2/20 fee structure might not appear to be much, however, in the end, it is definitely extremely expensive. Nonetheless, you can still get an 18% CAGR out of it which beats the most expected average market return.

If you add a zero to the initial fund, then you can add a zero to all columns except column (6) which as a percentage will not change. But adding this zero to all other columns will paint a much bigger picture. You might be able to get these numbers simply by having opted to put more effort into finding more capital from the start.

The above two charts also say that the major part of the rewards come from having a sustainable alpha. And mostly from having endured. Without this alpha, what would be left is column (1).

Therefore, I would conclude that the 2/20 fee structure is more than sufficient. With the uncertainty of what might be a portfolio's future outcome, it could also be considered excessive fees, almost highway robbery. Should the fee structure be higher, the picture gets even worse. But then again, they too, the fund managers that is, would have to last with their alpha to get these fees. If only all those portfolio managers could deliver!

But, what if they could not deliver? Some experts expect a 5% CAGR as market average for the next decade or so, some even less. How much alpha will they be able to extract from such a market?

What would I classify as the most important ingredients in all this? The initial stake, the alpha and mostly time. Charts #6 says: make your trading strategies last, make the alpha sustainable for a very long time. And get an appropriate initial stake to make it count.

To gain a better understanding, follow the cues, make the calculations yourself. You should reach the same conclusions I did.

Conclusion

The alpha is the excess return above average market returns. It could be worth paying for it if it was sustainable for a long time. A hedge fund 2/20 fee structure might at first appear reasonable, but when viewed from a long-term perspective, it could be quite expensive as illustrated above.

The most important ingredients to this problem are all in a simple future value compounding formula: F(t) = F0∙(1+ rm + α)t, where rm is almost free, and where the other ingredients depend on you. It is your initial capital F0, your ability to generate some alpha (your edge), and the length of time you will put in this investment/trading endeavor.

The following chart is the same as chart #1 in Part I. Only the scale has been changed to logarithmic. This way, an exponential curve as depicted in chart #1 becomes a straight line in chart #7.

 #7  10% CAGR – 20 Years – Log Scale
10% CAGR - 20 Years - Log Scale

(click to enlarge)

Those are still the curves being played. Just looking at the chart we should know exactly what to do. And that chart simply says: buy in, and right from the start. It might not seem to matter much which curve you will use, they both end up at the same place. The erratic path does not seem as pronounced as in chart #1 making the random wiggling around almost trivial.

What you should be debating is: do you do the job yourself, or let someone else do it for you?

Related articles:

A Price Tag on Alpha - Part I
A Price Tag on Alpha - Part II
Stock Portfolio Alpha Definition 


Created... October 12,  2017   © Guy R. Fleury. All rights reserved  

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