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Friday, November 9, 2007

Some thoughts on Position Sizing

“[Soros taught me] it’s not whether you’re right or wrong that’s important, but how much money you make when you are right, and how much you lose when you’re wrong.” – Stanley Druckenmiller

When novice invests in the stock market, they are usually full of hope and optimism. They tend to only consider the upside (and target price), and usually ignores stop loss, before putting on the trade.

Perhaps this is due to the prevalent myth of a “perfect stock-picker” or “perfect stock-tip” – the perfect investor or tip that always pick winners and never makes mistakes. Sadly, that is a myth. Invest long enough, and soon, everyone will have a loser in his hands. This is stock market reality. Show me someone who has made 100 trades with 100 winners and he/she is a liar. :-)

It is not common to read this, but even the Best of the Best, the master investor and the world’s 2nd (or 3rd) richest man – Warren Buffett – has made his share of investing mistakes and continues to do so even today. Don’t believe me? Well, take a look at this site and look at the first entry – BAC (Bank of America). BAC is a relatively recent purchase (mid this year), and to date, Buffett has an unrealized loss of 13%. So, even the Best in the world still makes mistakes.

So, if Buffett continues to make mistakes, and we lesser mortals also make mistakes, how is it that Buffett has managed to amass such a huge amount of wealth that far exceeds our own experience let alone our wildest imagination? Remember that Buffett starts from nothing, like most of us. What is it that truly separates Buffett from the vast majority of investors?

Well, we’ve heard many reasons mentioned elsewhere such as his unparalled ability to determine intrinsic value of a business, margin of safety, ability to accurately assess business future prospects and risks, ability to assess management honesty, integrity, competency, understand company financials and business models, amazing memory, his infinite patience to wait for the “fat pitch” even if it means waiting for decades for the right opportunity to come along, his people and business management skills, etc. etc. etc..

But despite all these wonderful abilities, the bottom line is he still makes mistakes. Period. His recent BAC purchase is a timing mistake – 13% loss. His recent Petro China sale at $12 which is well below the peak of $20 is a timing mistake. And many, many more. But despite these mistakes, how is it that he is worth billions of US$ and his millions of “twin investors” (in the same 55 years investing period) aren’t ?

I believe the main and the least understood reason is because he is also a Master in “position sizing”. Bottom line is that when (not if, but when) he makes mistakes, his mistakes tend to have minimal impact on his total capital. But when he is right, his bet has a huge impact to growing his net worth. He aims to preserve capital and score home runs by only betting big in situations that he has the most confidence in. And he avoids bets that don’t meet his strict criteria. When he is winning, he adds more to his winning positions including not selling his winners which has grown to become even bigger % of capital over long periods of time (e.g. Coca-Cola). When he is proven wrong (e.g. adverse earnings results on Pier 1), he doesn’t throw good money after bad ones by averaging down, but instead sell out.

Buffett is well known to have infinite patience and waiting for the “fat pitch”. What does a “fat pitch” means? Well, it is a baseball term, where the batter will only swing at the ball when it is at the most favorable zone. In other words, he will swing only when the ball is at the ideal position for the batter to score a home run. He will not swing until he gets the perfect pitch, or the “fat pitch”. In other words, he will only invest in situations that meet his strict and successful criteria.

But occasionally, he will be presented with more than 1 opportunity that meets his criteria. E.g. he may be looking at several eligible opportunities, each with different % return on capital. In such a situation, I believe Buffett will automatically puts bigger amounts on the higher % return on capital opportunities subconsciously and without hesitation. His frequently quoted yardstick is to always compare with his best existing investment (such as Coca-Cola). He will not invest in a new venture if the return on capital is lower than Coca-Cola. Instead, he will prefer to add more Coca-Cola if the pricing is right.

It is also worth noting his “buy and hold forever” approach. When he is right and a stock price starts to appreciate, does he sell? Unlike most of us, he doesn’t sell. Again, Coca-Cola is the most obvious example. He has held that stock for decades now that Coca-Cola has grown to become the number 1 stock holding for Berkshire for many, many years. As Coca-cola grows to become a higher % of Berkshire’s capital, he is happy to do nothing and just let his winners grow. He is not concerned that Coca-cola has grown to become “too large” a % of Berkshire’s capital. All he is concerned about is making a meaningful amount of money when he is right.

And indirectly, this is also a passive form of “position sizing” for him, since he continues to hold even bigger positions in his long-term winners like Coca-Cola which continues to make even more money over time.

So, what can we learn from the above? Can we break down the main principles of position sizing? How do we mortals decide how much to invest in a trade? To me, mathematically it boils down to 3 things:

1. The odds of winning and losing. Other things equal, you want to bet larger amounts in trades with the highest odds of winning. This means you must acquire and learn the ability to distinguish and rank trade opportunities since not all trades have equal odds all the time. And you want to avoid trades where the odds are simply 50/50 when you are simply uncertain. Here, Kelly’s Optimization Formula for even-money bets may be useful for value investors who like the precision of mathematical formulas. http://en.wikipedia.org/wiki/Kelly_criterion. In fact, the Motley Fool calls it “the Most Important formula in investing”. See http://www.fool.com/investing/value/2006/10/27/the-most-important-formula-in-investing.aspx.

2. Risk/reward trade-off. Besides the odds of winning and losing, there is also the amount which one expects to win when one is right (=Reward), versus the amount that one expects to lose if one turns out to be wrong (Risk Amount). Value investors demand bigger margins of safety to bet big, since the bigger the margin of safety, the bigger the potential reward and the smaller the risk. Traders sometimes calculate these as Reward = Target Price – Current Price, and Risk = Current Price – Stop Loss price. Mathematically, there is no real distinction between how a value investor and a trader calculates Reward – the difference is definition and semantics. Basically, other things equal, you want to bet bigger amounts when the Rewards substantially offset the Risks. The Kelly general formula gives an optimize formula to maximize equity growth to determine this.

3. Your accuracy in assessing 1. and 2. above. In the investment field, there are surveys and studies that show that most investors tend to over-estimate their ability in sizing up the winning odds, and tend to under-estimate the odds of losing. It’s a bit like surveys showing that most drivers tend to think that they have “above-average” driving skills – this is clearly impossible, since objectively, “the majority cannot be above-average”. For value investors, a formula like “half-Kelly” (or a fractional Kelly) could be useful here, to compensate for the initial over-estimation. As one becomes more competent later, the formula could be fine-tuned to tailor to the individual.

Whilst Kelly is typically applied to value investors, the 3 principles above can also be applied to traders, although the details usually differ due to the different approaches. E.g. for 1., some traders avoid trades with less than 60% (or another %) chance of success and only focus on trades with more than 60% chance of success, based on technical charts or some other criteria. For 2., some traders avoid trades when the Rewards are less than twice the Risk (or some other parameter). For 3., the actual position size is sometimes calculated based on a constant % of capital at risk approach (instead of Kelly’s). Basically, this approach starts off by setting a certain fixed % of capital which a trader is willing to lose from a trade if his trade goes wrong – typically, 0.5% to 2% of capital. E.g. if one has $100,000 capital and one is willing to risk 1% of capital or $1,000 in the event of a stop loss, then, the amount one would invest will depend on the gap between current price vs the intended Stop Loss. If the Stop Loss is near the Current Price, the position size is larger than if the Stop Loss is further away from the Current Price. E.g. if Current Price is $1, and Stop Loss is $0.90, then, the number of shares to buy = $1,000 / ($1 – 0.90) = 10,000 shares = $10,000 = 10% of capital. The idea is that if the stop loss is executed at $0.90, the loss = 10,000 shares x 0.10 loss = $1,000 = 1% of capital. This assumes perfect stop loss execution with no slippage. In reality, some allowance must be made for these. Depending on the perceived odds, they will vary the amount of capital at risk, such that on trades with the most confidence, one may place more capital at risk, and vice versa.

Some Concluding Comments

The concept of position sizing is not usually obvious to beginning and average investors. It is only too common to hear the average Bursa investors asking their tipster or “gurus” WHAT stock to buy. Visit any investing blogs with chatboxes, and the most popular question when it comes to tips by far may be “WHAT STOCK to buy?” The second and third most common question is “WHAT PRICE to buy and WHAT is the Target Price?” It is less common to hear “what is the stop loss price?”. And perhaps a question that we almost never hear is “how much” to buy, or what % of capital to buy. And unfortunately, the last question may in fact be the most important question of all, in terms of the impact on total equity growth.

Why? Well, imagine you’ve made 3 trades – the first 2 successful and the 3rd unsuccessful (67% success rate is not a bad rate). Let’s say 10% gain, 50% gain and 5% loss respectively. If your largest position is the 50% gain, then, you should come out well on your total equity. But if your largest position is the 3rd trade with 5% loss, and your first 2 trades are very small positions, then, you can actually end up with an overall net loss. Despite scoring 10% and 50% gains!

Don’t believe me? Well, prove it to yourself mathematically. Imagine you invest $3k each in the first 2 trades. And imagine you invest $50k in the 3rd trade. Your net loss is 3000 x 10% + 3000 x 50% - 50,000 x 5% = - $700 (or $700 loss).

So, in conclusion. As you become more competent in investing and trading, pay more attention to position sizing. Better, learn from the masters (whether master investor or master trader) how they approach the issue of position sizing.

On a personal note, I want to share with you my own personal investing experience recently which has convinced me the importance of position sizing. I am very proud to say that my recent Petrochina Call Warrants trades have given me the largest $ gains I have ever had from a single investment ever in my entire life. Petroch-C1 has the most amazing run from a low price of below 5 sen on Aug 17, to a high of $1.11 on Nov 5. I first entered PetroCh on June 8, but it was a very small position. On Aug 17, I managed to get a very small position at rock bottom prices, but sold too early, and then, kept buying more on its way up. On Nov 2, PetrochC1 & C4 represented nearly 30% of my entire capital! (this is by far the largest amount I have ever had on a single stock, when my previous principle is never to have more than 5% of my capital in any single stock, let alone a Call Warrant!). Finally, on Nov 5, due to its uncertain price action, I decided to sell all of my Petroch-CW holdings at around Nov 2 closing prices. In $ terms, the returns from Petro CW alone (in 3 months) is more than 3 times my largest gain to date then (MAYBULK, after nearly 2 years of value investing). There are 2 critical lessons for me from this experience. First, when you are right about a stock, don’t be afraid to keep adding more on its way up – I was adding Petroch-C1 at increasing prices, even when it was trading at 80+ sen at new highs. I have actually done this many times before with other stocks, but the difference with Petroch-CW is the stark difference in “position size” – I was around 80% confident in Petrochina, and according to half-Kelly’s formula, I should aim to have around 30% of my capital in it. Second, when you are in an uncertain position – and this happened on Nov 5 when the mother share could not sustain its rise past $20 – I quickly liquidated as much as I can. I had no business playing CWs when I am uncertain on its future outlook – again a Kelly formula with 50/50 odds suggests nil holdings. Again, I have practiced this many times before, but the difference this time is that I am willing to let go 100% (or as close to it as I can) when I am uncertain, as opposed to the normal practice of retaining half. And this is an important aspect of position sizing too. As a result of an overall much improved position sizing experience from entry to exit, I have already observed a substantial and almost immediate improvement to my own personal equity results.

It is also worth noting that I did reenter Petroch-C4 at prices between 65 to 70 sen after Nov 5 (after having sold them at close to 90 sen on Nov 5), but this time, because the outlook is much less certain, my position size is much smaller at less than a third of my original Petroch-C4 position. Naturally, I am expecting a worse price tomorrow due to the prior day weakness in HK, but in the worst case scenario (assuming I can execute my personal stop loss without much slippage), I still expect to keep around 90% of my Petroch-CW gains. From my peak gain in total equity in late July, my total gain is now close to double the peak in roughly 3+ months as a result of improved focus on position sizing. Naturally, I am happy with my Petroch-CW gains, but the personal satisfaction of a successful trade with improved position sizing is beyond description.

Good luck in your future trades.

Disclaimer: As usual, trade (buy, hold, sell) at your own risks.


jasonred79 said...

Well... Buffet has an unrealised loss of 13% on BAC, but a REALISED gain of, what, 700%- 900%, on PetroChina.
He spent apporximately the same amounts on his purchase of Petrochina and Bank Of America. ($450 million)
So, he lost $50m on BAC, but made $3 billion on Petrochina. ...

I hardly see how this sort of performance can be called anything short of "very profitable".

His decision to sell might be influenced by the following statement he made:
“It was an easy decision to buy PetroChina. It was one-third of what it was worth, maybe a quarter,” he said. “I doubt in the present market I would find something like that as the market has been too hot.”

in other words, he valued PetroChina at under HKD10.
So, in a sense, he bought when Petrochina was "cheap", sold when it was "slightly expensive", and is staying clear of it now that it is "very expensive".

Of course, his valuations could well prove to be wrong.
Buffet himself has since made comments that he *probably* (LOL!!!) sold Petro too early...

As for position sizing, Petrochina was worth around 1.5% of Berkshire recently. (Was worth around 0.25% of Berkshire at purchase IIRC)
In terms of STOCK portfolio, Petro was worth around 5% and 8% respectively I think.
IMHO, Berkshire is TOO BIG for position sizing.
IMHO, if he thinks it is good, Buffet just buys EVERY SHARE he can get his hands on.
If he thinks it is bad, he just doesn't buy it at all. (bear sterns, CFC, HOV etc)

One more bit to add on the whole "buying growth stocks" factor. As Buffet said, 10x5x3x2x0 is still 0.

HOWEVER. If your position size on 10 growth companies is equal, $10 becomes 1+5+3+4+0+0+0+2+3+7= 20. So, even though 3 out of 10 companies go BUST, you can come out doubling your networth.

jasonred79 said...

By the way, I haven't bought any BAC, and I don't plan to. HOWEVER... I do think that Buffet has a fair chance of making money on it, in the long term. Er. I mean Berkshire. BAC might not go green during buffet's lifetime. (touch wood)

I find Buffet's investment strategy to actually be very very simple: Buy into great companies, at cheap prices. Sell at high prices.

From what I hear, he doesn't actually have TIME for all the complicated stuff. He lives in a small house, lives a simple life, doesn't even bother turning up for most AGMs even though he is the chief shareholder for those major companies... overall, Buffet seems like a man who keeps things simple.

As for market timing... I've never even heard him mention a word about candlesticks or charting, so I suspect he doesn't bother with Technical Analysis at all.

Seng said...


Thanks for your comments and for highlighting Berkshire's huge PetroChina gains.

For discussion purposes, it's worthwhile to break his gain down into 2 elements - the Buy and the Sell.

Firstly, the Buy. Clearly, he bought the RIGHT STOCK at the RIGHT PRICE during Petro IPO. As a result of making the right buy, he reaps a huge reward. Why? I believe position size contributes to it. He was the 2nd largest shareholder of PetroChina, and that is not a small position. It is meaningful enough to make some difference to Berkshire's net worth. In other words, he aims to make a difference when he is right

Secondly, the Sell. As you pointed out, Buffett himself admitted that he sold too soon. I believe he realized himself that this part is a mistake.

Still, my point is that Master Investors put themselves in a situation where when they are right, they want to get the most out of the situation (e.g. Petro Buy), and when they are wrong (e.g. Petro Sell), it has minimal or no negative impact.


Seng said...

I should add that overall, I would be happy to achieve 10% of what he achieved with Petro China. I still think Buffett is a genius.

But for the purpose of learning from the Masters, he admitted himself that he probably made a mistake by selling too early.


Seng said...

And I should also add that this does NOT mean we should go out on a margin and scoop everything with both hands everytime we see a "compelling investment".


Because we are not Buffett in every other aspect. In terms of the 3 aspects to position sizing, Buffett is a genius in:
1. Sizing up the odds of winning.
2. Sizing up the Risk/Reward.
3. Having a very good assessment of his own ability in 1. and 2.

Whereas most of us "thinks" we are equally good, and in reality, don't come even close to the Master! :-)

Which is why a half-Kelly, or an even smaller fractional Kelly is desirable to keep us out of major trouble.


rask3 said...


Excellent post. Just would add a few words.

I believe, as a long a term investor, that if one had done the homework before buying a stock, the time to sell is almost never, assuming of course the stock posesses the requisite characteristics. Certainly, very, very few stocks would qualify for such an approach.

If you were the sole owner of an excellent company, would you sell it just because the Hang Seng index or the Dow Jones index has tanked yesterday? Put this way many would, of course say, no. The mere reason that one could buy and sell stocks at the touch of a few keystrokes doesn't mean dancing in and out of stocks is the correct approach. I believe the more decisions you force yourself to make, the poorer will be the final results. Of course, if someone has perfect foresight or unusual abilities this wouldn't apply to him.

Regarding Buffet's sale of Petrochina, I'm not sure why he sold though he has said that he sold because of valuation. Would he be proven right in selling if Petrochina didn't go up by much? Or if Petrochina had gone down? I think the near term outlook of the stock market or the near term outlook of a particular stock should not be the criteria for selling, if you're a long term investor.


jasonred79 said...

But... He bought 450m Petrochina, and he bought 450m BAC.

My point is that he bought exactly the same amounts. Despite the fact that he is VERY unlikely to reap the same returns with his BAC.

however, your point about position sizing is a good one for the small-medium trader. Without a doubt, the logical thing to do is to put in less money into a counter if you are less confident of it.

As for the whole Petrochina thing... let us go back to one of the top 10 lessons in Stock Market: Hindsight is 20/20, but predicting the future is very myopic and near blind.

I think it's a little early to condemn or rationalise Buffet's actions. (though as noted, he criticised himself already, lol). I think that we should merely look, study, and take notes, without actually passing judgement. In 1-2 years time, AFTER all the dust has settled, we can pronounce judgement.
I've seen too many Economists and so-called experts criticising rather controversial policies. Only to eat their words when said policies prove to work well beyond all expectations. (similiarly though, I equally often see them proved absolutely right. heh heh such is life)

Seng said...

Hi Jason,

I agree with the first half of your point that "Hindsight is 20/20, but predicting the future is very myopic and near blind." The latter is better read with a qualifier like "often" or "usually". It may seem nitpicking, but such small difference between often vs always can be exploited financially.

Notwithstanding this, the purpose of my article is not to criticize Buffett or to condemn him. It is not my intention. I'm actually writing this in a neutral tone, although written words might not be able to convey this.

As a trader, I believe every buy and sell decisions can always be improved upon, even when executed by masters. I think most market timer masters would agree with the view that his sale timing can be improved upon.

For Petro China, I think Buffett underestimated the euphoria as the time get closer to A share listing. As you know, quite a few of us on the chatbox profited from this.

His overall Petro trade is excellent. There is no question about it. When one makes 6 to 7 times profit in such a relatively short time, it is phenomenal.

Even if Petro China prices subsequently fell, the point remains that he made a timing mistake in selling a little too soon.

Of course, I could be wrong in the sense that maybe the market - upon seeing the initial sales by Buffett - hesitated to go up (even though the A share listing is widely anticipated). So, maybe Buffett felt pressured to sell before A share listing at whatever cost (as the price hesitated to move upwards). And then, the market was so relieved after he finally sold, that only after he sold completely, the price could go up. I.e. the counter-argument could be that he could never sell at the top since the market waited until he fully sold out befoe moving upwards.

Still I suspect this hypothesis is weaker, since Buffett himself admitted his timing mistake, that he sold too soon. But he also accepted this without any hint of negativity from the video that I watched. It is with the same acceptance non-negative tone that I write this comment.

Just want to clarify that this is not a condemnation of Buffett. Merely observation.


rask3 said...


I think Buffet's strategy could be as simple as buying undervalued stocks and selling them when they become fully valued or over valued.
I don't think he gives much importance to what the market will do soon after he had made the decision to either buy or sell.

It is impossible really for anyone to tell how high a stock could go after one has sold for the reason that the valuation is not justified on fundamentals. I wouldn't consider Buffet to have been smart if Petrochina had in fact tanked after he sold. And less smart because it went up after he sold. You just can't make all the money that can be made unless you have perfect foresight.