How Much Should You Invest in Stocks? The Art of Position Sizing in a Volatile Market
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Walk on the money for the rest of us. This is a personal financial on money, how IT works, how to invest IT and how to live without worrying about IT. I'm your host David is stein toys is episode four fifty one.

It's titled how much should you invest in stocks, the art of position sizing in a vital market. Back in the mid one hundred and ninety, one of the most successful hedged funds was long term capital management. The fund was founded in one hundred and ninety four by two nobel prizes, loyals miron shows and Robert Martin, along with a number of very smart traders from Solomon n.

Brothers, including john, mary weather and Victor hagan's. Initial amount of couple race was very large for a new hetch fund, a billion dollars. The returns in the first three years were incredible. The net of fee return from inception three thousand hundred and ninety seven was thirty one point two percent annualized.

The fund never lost money two months in a row and grew to seven point five billion dollars, one of the largest hedge funds in the world, even though I was closed to new investors since in one hundred and ninety five, long term, capital management investment approach exploited the Price differences between various financial instruments such as government bonds, corporate bonds, stocks, currencies. The strategy is known as relative value arbitral ge. And the idea is that while related securities, their Prices might diverge for a short time due to supply and demand and baLances, that ultimately the Prices converge to their true relative value.

Each individual bet on a zone if unlevel wasn't very risky, but the fund used a great deal of leverage in order to magnify the returns of these small bets. The strategy obviously worked very well until IT didn't. In August one nine hundred eighty eight, russia defaulted on its government that Sparking a great deal of financial turmoil and volatility.

For example, the msci emerging markets index fell twenty nine percent just in the month of August nineteen ninety eight, and the markets move the different asset types that long term capital management was using in its strategy that the moves were extreme, much greater than their models assumed. And as a result, long term capital management last ninety percent, the new york federal serve organized a consortium of large counterparties, investment banks, commercial banks that traded with long term capital management that were exposed to huge losses because they had provided leverage to a long term capital management. And the new york fed organized basically a bail out where those counterparties invested three point six billion dollars in the fund and got ninety percent ownership and at time for the fun to be liquidated.

And in the end, those investment banks had invested, earn ten percent on their capital, but not the general partner, nor the limited partners in long term capital management. Vitor hagan, I said he personally lost over one hundred million dollars in that fun, he wrote. I was thirty five years old at the time, the Youngest of the long term capital management partners.

I saw that all my partners, many whom like family to me, also thought the fund was a very attractive investment. On top of all this, the fund was far from a black box to me. In fact, IT was the investment that I understood the best of all things I could possibly invest in.

Hagan, I was trying to figure out what percent of his wealth should he invest in this investment that he understood and was poised to do extremely well. He continued. The end, I had to decide on something.

I felt that no matter how attractive and investment opportunity might be, I want to keep an amount on the side invested in the safest acid possible that would support about forty to fifty years of what my family was spending at the time, even if the fund lost one hundred percent, which he lost ninety percent, and he lost all of his investment. And at the end of the day, he said asi twenty percent of his net worth and then put eighty percent in the front. A few years after the fund exploded hagon, I wrote, after more than twenty years in finance, you'd have thought that i'd figure out how to invest my family savings.

Well, IT was two thousand and two. I just turned forty, and I had and lost over one hundred million dollars. And so spent a number of years thinking about this scaling problem.

How much should individuals and families invest in a risky opportunity in those four, five years of thought? Hagi realized that passive investing, index investing, lowers costs between no, but in in more dynamic markets can lose money, particularly stocks, but that a black box strategy like long term capital management can be complicated and costly, and after that, those huge losses and long term capital management may not be appropriate for his family's wealth. Haganah launched l partners and recently published a book with his colleague James White.

The book is titled of the missing billion's i've been reading IT and IT. It's a fascinating book, one that i'm going to add to the list on our website of recommended books on investing in the economy. It's an intriguing title.

The missing billionaire, they point out if we go back to the one thousand hundred, the U. S. Senses recorded four thousand american millionaire haggan I.

White said that if even a quarter of those millionaire in thousand nine hundred had started with, lets say, five million dollars and invested in conservatively over the years, earning a reasonable way to return, there should be sixteen thousand old money billionaires in the us. In reality, according to force, there's only seven hundred billionaires total, not one of which can trace their assets back to a million years. Ancestor in one nine hundred, all that wealth dissipated over the decades.

And he was IT because the wealth was given away. IT was lost, either spent or not invested. appropriate. In the new york times, I recently saw the arbitrary of chard's fini, who was a billion air worth up to eight billion dollars.

He passed at age ninety two and gave away all of his wealth he found when he was age fifty and had homes in new york, london, paris, hanoi and ford, cisco, asma, colorado and france, living an abul ent lifestyle that is just didn't make him happy. In the biography written about him, conor o. Clery wrote he was beginning to have doubts about his right to have so much money.

He said aside, two million dollars for him, self money for his kids, and then gave IT all away. Most of IT anonymous. Ly, there are not buildings named after Charles fini. Most billionaire don't do that. Victor hagon, I lost hundred million dollars fortune in long term capital.

So they wrote this book because they point out that we spend a lot of time discussing what should we buy, which investment we should buy, but don't spend as much time. And perhaps a more important question, how much should we put in one investment? I've discussed this in an epsom in the past, an episode two fifty investing rule one, avoid ruin, and said, we need to build buffers, protections, additional savings.

We get insurance, we build redundancy, so that ultimately we can live a well lived life and we avoid financial ruin. IT can just be stocks for the long run. Yes, stocks may outperform bonds over the long term.

But would I put one hundred percent of my portfolio and stocks? No way. I want multiple drivers. And I want to understand what the building blocks of of those return drivers are.

What has to happen for me to be successful and not put all the eggs in one basket? Long term capital management investment bounce back. They came back, but not for the limited partners that were White out or for the general partners, hagan's and White, right? The short run always comes before the long run.

And neither of us got to enjoy the rebound of these investments. The lesson, good investments plus bad sizing can result and catch clisson c losses. In their book, they share a study that a Victor and a corey archer, which are we published in two and thirteen in the journal of portfolio management, he didn't experiment where there were sixty one financially.

A stood individuals playing a simple coin flipping game, and IT was a virtual coin, and the coin was set up that IT had a sixty percent chance of landing on heads. The participants were given twenty five dollars and allowed to bet any way that they they wanted to bet, how much they wanted to bet in. Each took around for thirty minutes.

They could bet one after the other and decide how much they wanted to bed. This game had a sixty percent probability of success. IT had a positive expected return that meets our definition of an investment, an opportunity with a positive expected return.

Yet thirty percent of the participants lost some money, and twenty five percent lost at all. Only twenty percent made IT to the maximum that you could earn in the game of two hundred and fifty dollars. Now you can try this yourself at l wealth dot coms lash coin hive and flip C O I N dash flip that at l wealth dot come.

I tried IT myself before I continued reading in the book. I wanted to kind of figure out, how would I go about this problem started with twenty five dollars, and I started betting ten percent of the amount that I had until I got over thirty dollars. And then I began to beat twenty percent.

I'd played IT two or three times. And the one time I got very close to two hundred and fifty dollars, the other time I was around one hundred. One difference in the online game, you want to get ten minutes.

And the longer you play, if if you bet wisely, the higher the likelihood of getting to two hundred fifty dollars. But IT IT can be frustrating, because if the first series of coin flips went against me, then the amount would get less than twenty five dollars. And there is a temptation, SHE is bt, more so I can make up my losses.

Interestingly, they found that sixty seven percent of the party, the pants, even though they knew that the coin was weighted, sixty percent had they bet the tales anyway, because have to a series of heads, they thought that tales were do. But if something is waited, sixty percent chance of success. We do not want to bet on the thing that's only forty percent in the book.

They equate the stock market statistically, they do the analysis to determine that the stock market is like a coin that waited sixty five percent heads, thirty five percent taes. So not that much different than the sixty forty experiment. Probably the most important take away from the book for me, and a principle that I ve emphasized in earlier episodes of the show, typically, epa two fifty on avoiding room, and episode three fifty six on rebalancing hagan's White, for example, of a different game, a million dollar portfolio, twenty five coin flips, sixty percent chance of coming up pets.

And they went through the analysis that they show a table of the waited average expected wealth, different strategies of betting, one percent. The portfolio value, each time up to one hundred percent. Surprisingly, the expected wealth of bedding, one hundred percent.

Of the portfolio was ninety four million dollars. Why was that? Whether is that? Very, very small chance i've getting twenty five heads in a row, but that's expected value. The medium outcome, the middle outcome was losing IT. All because if you bet one hundred percent and IT turns up tails and then you're completely out.

But what about a more reasonable? But what about fifty percent of the wealth being invested still aggressive? The expected value of investing fifty percent is ten point eight million, pretty tractive.

But the medium out, the median outcome would have been only four hundred and twenty seven thousand dollars. How is IT that? We can have a high expected value, but the median result is much, much lesson that actually losing money.

We've touched on this in the past, particularly a paper by all Peters and merri government, called valuation gambles dynamics. And they point out that gambles, which is sort of ufos m form and investment in economics, are often considered one shot game. So maybe we will do a money carlo analysis.

So every time we start over to see how we will turn out in real life for passing through time, we don't get another shot at IT. If we bet our million dollars on a coin flip and we lose, we don't get to do IT again. Or if we lose one hundred million dollars in our hedge fund, we don't get that money back.

And so what happens through time is very important in the amount of wealth we have depends on what is happening through that series of returns. And so when we invest forty to fifty percent, let's say we're investing fifty percent, we have a million dollars. We flip the coin that turns up heads.

Now we have one point five million dollars, fifty percent gain. But then we flip IT again the coin, and that comes up tails when we lose fifty percent. Now we're down to seven hundred and fifty thousand dollars.

So we get a left when we get a head, but there's a drag when there's a tail. And this drag it's hard to make up. If you've lost fifty percent of portfolio, you have to gain one hundred percent to get IT back.

This is called volatility drag. It's because of what is known as positive scenes. When something is positively stewed, the average expected outcome, like in the coin flip, will be higher than the median outcome because of the extreme upside events that happened that pulls up the average.

And the higher the volatility, the more risky something is, the more secured gets to betting. Fifty percent on a coin flip will have more volatility drag more positive skies. And the median outcome will be much, much less than the average outcome.

This is important when we think about portfolio sizing because the more risk we take, the more likely that the amount of wealth we have the meeting an outcome will be much less than, let's say, the expected return, but the expected outcome. Before we continue, let me post and share some words from this week sponsors. Before we continue, let me post and share some words for one of this week sponsors net sweet.

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That's linton. That comes last, David, to post your job for free terms and conditions apply the way that we manage this volatility, this volatility drag this positive skin is to make sure that we are positioned appropriate in the amount of risk that we're taking. They share A A formula in the book that is derived from the work of Robert Martin, the economist, the nobel prize winning economist, the same that cofounded long term capital developed a formula for helping us determine what percent of our wealth should we invest in a risky asset.

What surprising about this is that even though he developed a formula, they didn't use IT. Well, maybe they did use IT in long term capital management, but the volatility turned out to be much greater than what they assumed in their models. And the correlation between the different asset types such that the fund blew up because of the leverage.

This formula is called the merton share. IT says that the optimal percentage of our wealth that we should invest is a function of the expect or return after backing out the risk free rate, so in the case of stocks of the elective return is eight percent and the risk free rate on t bills is two percent, then that's an expected return of six percent. So that's the numerator.

And then we divide that by a volatility figure. In this case, the variant, which is the square of the standard deviation, is a standard measure of volatility times, a risk version factor, which i'll get to an in a moment. But if we take our risk version times the volatility of an asset and we divide that into the expected return, that gives the percentage wealth that we should have invested in stocks.

For example, based on that formula, the greater the volatility or the greater our risk aversion, the smaller the position size that intuitively makes sense, or the greater the expected or return, the larger the position size. I actually plug some numbers in to this formula. So if we have an expected or return of stocks of eight percent and the risk free rate is two percent, and we assume the standard deviation of stocks is nineteen percent, which what has been historically.

So that's a volatility for you and assume a risk aversion of two. You can explain to in a moment it's one of the chAllenges with this is all, how do I know what my risk aversion is in my two or three? We get to that.

But if we asked the risk version are too. The formulas says we should have eighty three percent stocks and seventeen percent in the risk free asset. And if our risk aversion is three, using those same assumptions, that we should only have fifty five percent stocks.

So again, of the greater risk aversion, the lower we have in the risk asset. The other thing though, that if the risk free rate is higher, like IT is today, we should have a lower a mountain stocks. So if you soon and expected return for stocks of eight percent, so it's three percent after backing out the five percent risk free rate.

And our risk risk aversion is too, the formula says we should have forty one percent stocks down from eighty three percent stocks when the risk free rate was two percent, and then if our investment has an expected return of eight percent before backing out a two percent risk free way, but the volatility is thirty percent, the standard deviation and a risk aversion of two, then we should only have seventeen percent in risky assets. Now, the idea here isn't so much for you to memorize the formula, but to understand, based on financial theory, how much should we have invested in risky assets? Clearly, it's a function of a risk aversion, but it's also a function of the level volatility and if the expected return.

And so when an expected return is lower, when stocks are more expensive and they're expected returns are lower than we should have a lower allocation to stocks or when the risk free rate is higher, such as today, when we can earn two and a half percent plus inflation investing in treasury inflation protected securities, then that suggests we should have less in stocks and more in that risky asset. They also point out that if it's an active manager that's charging a one percent fee that requires a higher expect or return and potentially higher risk, which suggests a more concentrated portfolio. So the amount allocated to an index fun and stocks versus a active metric n, we would have a lower allocation in the mutual fund because the expecting volatility would probably be higher because it's more concentrated and the return might be lower because of the higher fees.

So this gets to the whole concept of dynamic allocation, and that's how i've invested my entire professional career and and my personal assets being willing to adjust the allocation based on changing expectations and changing risk. There's theories that back that i've never used the merton share formula before, but IT is in the trigger example, figuring out or what should be appropriate allocation. Risk aversion is an individual thing, but IT turns out that most people fall between a wine and a five and the average, as you would expect to sort of a two, two or three at.

In this example, we use the risk version factor of two and three. That's fairly Normal. What's behind IT? How do we determine a risk aversion? Well, IT IT gets to this concept was called diminishing marginal utility of consumption.

The more we have and the more we spend, the less happy we get by spending a little more or by having a little more. Having one billion dollars could be life changing. Having two million is less light changing than getting the first mine.

Likewise, eating our first pizza can feel wonderful. We had, we had pizza in the bedford park area of london, the best Peter of hat. First one, I probably would not have gotten as much joy out of the second week that would be so full.

That level of how four we are. Our happiness is known as utility. How much utility do we get? How much pleasure do we get out of getting more money or spending that money? And that really ties into a risk version.

And IT can change based on how old we are. IT can change based on economic conditions or recent experience, but IT isn't something that we should ignore. We should be aware of risk aversion, and it's not an exact science in some ways, we have an actual to feel for.

They give an example, they did a survey to sort of quantified what's the right amount of risk aversion to ask three questions, if you flip a coin, and this would be an equally waited coin, so no bias. And if you flip IT, you lose ten percent of your wealth. And so then they ask, what percent would you need your worth to grow if IT went the opposite? So head, you lose ten percent tails.

How much do you need in order to actually play the game? And most people responded that they would need at least a twenty percent gain in order to do that, twenty percent upside for the risk of losing ten percent on the downside. They asked how much you I did on the upside, if you lost twenty percent on that coin flip.

And most people, once the loss has got greater, they needed more upside. They needed fifty percent upside in order to be willing to risk twenty person of the wealth. Then they, they asked the opposite question, if the coin comes up heads, your wealth would increase five times five fold.

How much downside would you be willing to risk of your wealth if he came up tails? And most people said thirty percent, and they they quantified IT. And at the end of the day, they realized that most people, and based on that survey, come in with a risk aversion level of three.

The author is find that they're two, so most of us are two to three. And and so you could use this formula, the merton share formula, to calibrate how much goes into stocks. And you use two to three as the risk factor.

Now some, we're gonna even more risk averse. So the higher the number, the higher the risk aversion factor the last set gets invested in these risky assets. So what's our take away where there's three? First, we need to understand our risk aversion.

What's our a level of contentment with our current levels of spending and wealth? How much regret would we feel if we'd suffer a twenty percent loss? How much upside that we would need in order to take those type of decisions? And there important because sometimes we get really entrance by a huge potential upside and investment, but it's very, very valuable.

IT can be enticing, but the higher the volatility, the lower we should invest because that's our second point. Our allocation to risk our assets should be based on the expected return for those risk of the asset. But what is IT relative to the risk free rate? And if we can earn five percent on cash right now, that means unless the expected or return for stocks has increased the hurt rate to increase our allocation, the stocks is much higher.

Now we should have more in lower risk assets. And the theory backs that in initially. Ly, that feels good. And then the third point is the more risk we take, the greater the volatility.

The greater the volatility drag, and the more as we pass through time, we should focus less on the expected or return and more on the meeting outcome. Recognize that yeah maybe on average, this is what people did in terms of expectation. But if that averages pulled up because of some did incredibly well, then we should focus on the middle outcome.

And it's not just investing. Think about writing a book. Very few best sellers out there, but those that have a best seller, their earnings are so much greater that they bring up the average.

So the average earnings from a book is much higher than the median earnings. So we should focus on what's the median person doing and then make our decisions that way as opposed to what the average is. And this is especially important when IT comes to to financial decisions as well as time.

That's our discussion on position sizing what percent of our wealth to invest in risk your assets. The book is titled the missing billionaires by Victor hani and James White, that episode four fifty one. Thanks for listening.

I have loved teaching you about investing on this podcast for over nine years. Some topics though I just Better explained in writing or with the chart. And that's why we have a weekly free email newsletter, the insiders guide in that newsletter.

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