Why are you not compensated for taking unsystematic risk?

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Why are you not compensated for taking unsystematic risk?

Post by steve321 » Tue Sep 04, 2018 2:16 am

The following piece of advice has been given to me, on the question of whether buying individual stocks makes sense:
The main thing is that you would be taking unsystematic risk. Because unsystematic risk is diversifiable, you are not compensated for taking this risk.
I found this quote very interesting (and a bit puzzling) and I thought this question deserves consideration from a theoretical perspective: can anyone explain why investors are compensated for taking systematic risk (I take it to mean the risk associated with the whole market(?)), but not unsystematic risk (I take it to mean risk of individual stocks)?
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Re: Why are you not compensated for taking unsystematic risk?

Post by ThrustVectoring » Tue Sep 04, 2018 2:38 am

The return of a diversified portfolio is simply the weighted average of the return of the various stocks you hold. If you take all the stocks of a diversified portfolio and hand each individual one to a different investor, the average return stays the same because you have the exact same securities. The risk being taken, on the hand, goes up - some investors do very well, others get ruined. The variance of the portfolio as a whole is significantly lower than that of the individual pieces.

So that's why there's no compensation for unsystematic risk: you're still holding stocks, on average holding stocks gets you average return, and you're taking more risk.

Systematic risk is compensated because otherwise, people would buy lower-risk assets (treasuries) and get the same return with less risk. So the price of risky assets falls until individual investors no longer have a preference between the two.
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Re: Why are you not compensated for taking unsystematic risk?

Post by steve321 » Tue Sep 04, 2018 3:01 am

ThrustVectoring wrote:
Tue Sep 04, 2018 2:38 am


Systematic risk is compensated because otherwise, people would buy lower-risk assets (treasuries) and get the same return with less risk. So the price of risky assets falls until individual investors no longer have a preference between the two.
does this concept correspond to the equity premium risk? I remember that Mr Swedroe wrote that in 2000 (or 2001?) the yields of TIPS was higher than the E/P of stocks, so there was no equity premium. So basically does this means that at times things get out of line and you're no longer compensated for systematic risk?
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Re: Why are you not compensated for taking unsystematic risk?

Post by JoMoney » Tue Sep 04, 2018 4:49 am

There's an awful lot of professionals making bets in the market expecting their opinion is better than someone on the other side of their trade. Unless you have unique information or a market position that is giving you a unique advantage, why would you expect the stocks you select to have higher returns at a lower risk?
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Re: Why are you not compensated for taking unsystematic risk?

Post by steve321 » Tue Sep 04, 2018 4:59 am

JoMoney wrote:
Tue Sep 04, 2018 4:49 am
There's an awful lot of professionals making bets in the market expecting their opinion is better than someone on the other side of their trade. Unless you have unique information or a market position that is giving you a unique advantage, why would you expect the stocks you select to have higher returns at a lower risk?
Yes, but I was not asking whether individual stocks can produce higher returns at a lower risk. I was asking why they have uncompensated risk, i.e. as far as I understand, you take on extra risk but are not compensated for it. So according to this argument, they should have a lower risk-adjusted return than the whole market. Is that right?
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Re: Why are you not compensated for taking unsystematic risk?

Post by JoMoney » Tue Sep 04, 2018 5:52 am

steve321 wrote:
Tue Sep 04, 2018 4:59 am
... So according to this argument, they should have a lower risk-adjusted return than the whole market. Is that right?
Yes, that is the theory, and tends to be the case in practice. The academic dilemma starting with that premise though is in finding a measurement to quantify the "risk".
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Re: Why are you not compensated for taking unsystematic risk?

Post by nisiprius » Tue Sep 04, 2018 5:52 am

Because you don't need to take it. You can diversify this risk away. Why should unnecessary risk be rewarded?

See, for example, Chapters 8 and 9 of Burton Malkiel's book, A Random Walk Down Wall Street.

Always with the proviso that this is theory which may or may not be true in the real world, you have to start by asking why risk should be rewarded in the first place.

Suppose you are at an auction and people are bidding on three items. Here is a key point: people are only allowed to make one bid at the auction, and there will only be one auction of this kind, or anything like it, ever. Assume that the bidders are rational, there is no sentimental value, they are traders who expect to sell the item again at some point, and they are in it to make money. But this is a once-in-a-lifetime maneuver, they aren't going to auctions like this all the time.

Item X is a transparent plastic box, essentially worthless in itself, but containing a $100,000 in guaranteed-genuine $100 bills.
Items Y and Z are opaque boxes. They come with a legal document that says that one of them contains $200,000, but not the other, and nobody knows which.

I hope we can agree that the true value of box X is $100,000.00, and that if bidders are calm and rational, the auction price will be very slightly under $100,000.00 (minus whatever razor-thin difference is needed to motivate people for their time and trouble). Maybe people demand an 0.1% profit even though they are taking no risk, so the final auction price might be $99,900.

What about box Y? Your mathematical expectation is exactly $100,000.00, but it's not a sure thing. You aren't in it for the thrill, and you don't have any inside information or hunches that let you guess which box contains the $200,000. I don't think you want to bid $100,000 or anything close to it. A 50% chance at $200,000.00 isn't worth $100,000.00 if you only get to do it once in your life. You want to be compensated for taking the risk. That means that, sure, you might take a shot at it and put in a bid of $90,000, because your mathematically expected return is $100,000 or +11.1% over your bid. However, as the bidding gets higher and higher, you and everyone else will drop out long before the price reaches $100,000, because the bidders demand to be compensated for their risk. Depending on what other opportunities are available elsewhere, you might actually be the high bidder at $90,000. You might actually get a box with a 50% chance of $200,000 in it for $90,000. It's possible.

The reason this is true is that I've set up a situation where people were forced to take the risk, and demanded to be compensated for it.

Now, consider a new auction with new rules: you're allowed to make as many bids as you like. Unfortunately, all personally have with you is your life savings of $100,000 with you, while your competitors have unlimited money. (That, by the way, is one thing about our hypothetical system that is quite a lot like the real world).

As before, the true value of box X is $100,000 and the bidding will almost reach $100,000, maybe $99,900.

As before, the mathematically expected value of box Y is $100,000, but this time, there is a difference. All of your competitors are able to diversify away their risk completely by bidding on both box Y and box Z. They are guaranteed to get $200,000.00, sure thing, by doing this. What is going to happen? Obviously, the price on each box will get bid up to almost exactly $100,000, maybe $99,900. For the bidders who can afford to diversify, there is no longer any risk.

But, you are sitting there with only $100,000, unable to bid on both boxes Y and Z. For you, then, the situation is the same as in the first auction. If, based on whatever personal equation you use for pricing risk, you were only willing to bid $90,000 then, you should only be willing to bid $90,000 now, because it is exactly the same situation for you as it was before.

So, there you are, sitting there, and you say, "Hey! I am taking more risk than everyone else, I deserve to be compensated for that risk! I am bidding $90,000 and I expect everyone else to drop out of the bidding, it's only fair!"

And everyone else is going to say "Sorry, that box may only be worth $90,000 to you, but it is worth $100,000 to me and I'm willing to bid up to $99,900. Tough."

So, in theory, equilibrium, rational investors, blah blah, most people in the stock market are diversifying, and are therefore taking less risk than people who aren't, and are therefore willing to pay more than people who aren't. And, the stock market being an auction, the prices rise to what most people are willing to pay. And in the mass that represents the prices that reflect the lower risk experienced by investors who can and do diversify.

The point is this. You hypothetically hold only, was it Apple and Amazon? As an investor in the Vanguard Total Stock Market Index Fund, I hold Apple, Amazon, and 3,562 other stocks. I have "only" the general risk of the stock market as a whole. IMHO that's a lot of risk, but you, obviously are taking more risk than I am. However, you and I pay exactly the same $2,012-or-whatever/share for Amazon stock.

We are paying exactly the same price for exactly the same stock. Just why or how is it that you think you are going to get an extra reward for putting all your eggs in two baskets, when you don't need to? Do you think a broker is going to say "I see you have decided to take a gamble so I am going to give you a discounted price that stock so that you will be justly rewarded for your extra risk?"

That's the theory, anyway.
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Re: Why are you not compensated for taking unsystematic risk?

Post by steve321 » Tue Sep 04, 2018 6:26 am

nisiprius wrote:
Tue Sep 04, 2018 5:52 am
Because you don't need to take it. You can diversify this risk away. Why should unnecessary risk be rewarded?

See, for example, Chapters 8 and 9 of Burton Malkiel's book, A Random Walk Down Wall Street.

Always with the proviso that this is theory which may or may not be true in the real world, you have to start by asking why risk should be rewarded in the first place.

Suppose you are at an auction and people are bidding on three items. Here is a key point: people are only allowed to make one bid at the auction, and there will only be one auction of this kind, or anything like it, ever. Assume that the bidders are rational, there is no sentimental value, they are traders who expect to sell the item again at some point, and they are in it to make money. But this is a once-in-a-lifetime maneuver, they aren't going to auctions like this all the time.

Item X is a transparent plastic box, essentially worthless in itself, but containing a $100,000 in guaranteed-genuine $100 bills.
Items Y and Z are opaque boxes. They come with a legal document that says that one of them contains $200,000, but not the other, and nobody knows which.

I hope we can agree that the true value of box X is $100,000.00, and that if bidders are calm and rational, the auction price will be very slightly under $100,000.00 (minus whatever razor-thin difference is needed to motivate people for their time and trouble). Maybe people demand an 0.1% profit even though they are taking no risk, so the final auction price might be $99,900.

What about box Y? Your mathematical expectation is exactly $100,000.00, but it's not a sure thing. You aren't in it for the thrill, and you don't have any inside information or hunches that let you guess which box contains the $200,000. I don't think you want to bid $100,000 or anything close to it. A 50% chance at $200,000.00 isn't worth $100,000.00 if you only get to do it once in your life. You want to be compensated for taking the risk. That means that, sure, you might take a shot at it and put in a bid of $90,000, because your mathematically expected return is $100,000 or +11.1% over your bid. However, as the bidding gets higher and higher, you and everyone else will drop out long before the price reaches $100,000, because the bidders demand to be compensated for their risk. Depending on what other opportunities are available elsewhere, you might actually be the high bidder at $90,000. You might actually get a box with a 50% chance of $200,000 in it for $90,000. It's possible.

The reason this is true is that I've set up a situation where people were forced to take the risk, and demanded to be compensated for it.

Now, consider a new auction with new rules: you're allowed to make as many bids as you like. Unfortunately, all personally have with you is your life savings of $100,000 with you, while your competitors have unlimited money. (That, by the way, is one thing about our hypothetical system that is quite a lot like the real world).

As before, the true value of box X is $100,000 and the bidding will almost reach $100,000, maybe $99,900.

As before, the mathematically expected value of box Y is $100,000, but this time, there is a difference. All of your competitors are able to diversify away their risk completely by bidding on both box Y and box Z. They are guaranteed to get $200,000.00, sure thing, by doing this. What is going to happen? Obviously, the price on each box will get bid up to almost exactly $100,000, maybe $99,900. For the bidders who can afford to diversify, there is no longer any risk.

But, you are sitting there with only $100,000, unable to bid on both boxes Y and Z. For you, then, the situation is the same as in the first auction. If, based on whatever personal equation you use for pricing risk, you were only willing to bid $90,000 then, you should only be willing to bid $90,000 now, because it is exactly the same situation for you as it was before.

So, there you are, sitting there, and you say, "Hey! I am taking more risk than everyone else, I deserve to be compensated for that risk! I am bidding $90,000 and I expect everyone else to drop out of the bidding, it's only fair!"

And everyone else is going to say "Sorry, that box may only be worth $90,000 to you, but it is worth $100,000 to me and I'm willing to bid up to $99,900. Tough."

So, in theory, equilibrium, rational investors, blah blah, most people in the stock market are diversifying, and are therefore taking less risk than people who aren't, and are therefore willing to pay more than people who aren't. And, the stock market being an auction, the prices rise to what most people are willing to pay. And in the mass that represents the prices that reflect the lower risk experienced by investors who can and do diversify.

The point is this. You hypothetically hold only, was it Apple and Amazon? As an investor in the Vanguard Total Stock Market Index Fund, I hold Apple, Amazon, and 3,562 other stocks. I have "only" the general risk of the stock market as a whole. IMHO that's a lot of risk, but you, obviously are taking more risk than I am. However, you and I pay exactly the same $2,012-or-whatever/share for Amazon stock.

We are paying exactly the same price for exactly the same stock. Just why or how is it that you think you are going to get an extra reward for putting all your eggs in two baskets, when you don't need to? Do you think a broker is going to say "I see you have decided to take a gamble so I am going to give you a discounted price that stock so that you will be justly rewarded for your extra risk?"
That's the theory, anyway.
That's a good explanation, thank you for taking the time, I appreciate it. So basically using your example someone buying only one stock might end up making a lot more profit (like if I buy one box for 100k$ and it turns out to be the one worth 200K$) but may also have a much bigger loss (if instead it turns out to be worth nothing). So yes one might be shooting for the stars and end up in the gutter.
Wisest way is to diversify, now I see that; I am still not sure whether you need to get as many as 3,564 stocks or whatever (also because if you index most the contribution to your fund actually comes from the big stocks) but if you can get them cheap in an ETF I guess why not?
Basically one problem I have with indexing is that I personally don't find many boring Uk companies attractive compared to Amazon, it just seems a waste of money to invest in them. But then I guess the Boglehead answer is that the market has priced all those companies efficiently to reflect their prospects, so it would be arrogant to think that I know better.
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Re: Why are you not compensated for taking unsystematic risk?

Post by Call_Me_Op » Tue Sep 04, 2018 6:39 am

If the variation - or noise - is uncorrelated between securities, then the more securities you hold the higher the signal to noise ratio. This is because the signal (or the long-term trend) adds directly while the noise adds in quadrature (that variances add directly). This is a basic result of the theory of signals buried in noise (stochastic processes).
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Re: Why are you not compensated for taking unsystematic risk?

Post by Tamalak » Tue Sep 04, 2018 7:09 am

You are rewarded for taking unsystemic risk, if you have good reason to believe that the individual stock you're buying is too cheap. This is called price discovery. Investing this way is so difficult, it's basically an entire job, though. Without the skills for price discovery, you have no business buying individual stocks so you won't be rewarded for it.

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Re: Why are you not compensated for taking unsystematic risk?

Post by steve321 » Tue Sep 04, 2018 7:30 am

Tamalak wrote:
Tue Sep 04, 2018 7:09 am
You are rewarded for taking unsystemic risk, if you have good reason to believe that the individual stock you're buying is too cheap. This is called price discovery. Investing this way is so difficult, it's basically an entire job, though. Without the skills for price discovery, you have no business buying individual stocks so you won't be rewarded for it.
That sounds the same as value investing: is it the same thing? At least that's what I understand Warren Buffett has done to get very rich: buying stocks cheaper than what they are actually worth.
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Re: Why are you not compensated for taking unsystematic risk?

Post by Call_Me_Op » Tue Sep 04, 2018 7:34 am

Tamalak wrote:
Tue Sep 04, 2018 7:09 am
You are rewarded for taking unsystemic risk, if you have good reason to believe that the individual stock you're buying is too cheap.
Just because you believe the stock you're buying is too cheap does not mean it is. The fact that the price of any given security is believed to be cheap by some people and expensive by other people is why the price goes up and down. This does not change the fact that on average, you are not rewarded for taking unsystematic (company-specific) risk.
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Re: Why are you not compensated for taking unsystematic risk?

Post by steve321 » Tue Sep 04, 2018 7:42 am

Call_Me_Op wrote:
Tue Sep 04, 2018 7:34 am
Tamalak wrote:
Tue Sep 04, 2018 7:09 am
You are rewarded for taking unsystemic risk, if you have good reason to believe that the individual stock you're buying is too cheap.
Just because you believe the stock you're buying is too cheap does not mean it is. The fact that the securities are believed to be cheap by some people and expensive by other people is why the price goes up and down. This does not change the fact that on average, you are not rewarded for taking unsystematic (company-specific) risk.
this seems to imply that the consensus is better than the informed opinion of some people. Surely in other areas of life this is not the case: if you want to build an airplane you don't go asking everyone for an answer to the math problems you need to solve and base your answer on the consensus, but you rely on those who know about fluid dynamics.
So why should the consensus in the markets be necessarily right? At least in real estate it's possible to make good bargains if you are smart enough, so I guess it should be possible in stocks too, perhaps particularly in small stocks.
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Re: Why are you not compensated for taking unsystematic risk?

Post by Call_Me_Op » Tue Sep 04, 2018 8:02 am

steve321 wrote:
Tue Sep 04, 2018 7:42 am
Call_Me_Op wrote:
Tue Sep 04, 2018 7:34 am
Tamalak wrote:
Tue Sep 04, 2018 7:09 am
You are rewarded for taking unsystemic risk, if you have good reason to believe that the individual stock you're buying is too cheap.
Just because you believe the stock you're buying is too cheap does not mean it is. The fact that the securities are believed to be cheap by some people and expensive by other people is why the price goes up and down. This does not change the fact that on average, you are not rewarded for taking unsystematic (company-specific) risk.
So why should the consensus in the markets be necessarily right? At least in real estate it's possible to make good bargains if you are smart enough, so I guess it should be possible in stocks too, perhaps particularly in small stocks.
What does the "right" price mean? The market price is set mainly by thousands of high-power fund managers and institutional investors. It is "the" price. There is no price that can be more "right" because this is the consensus estimate of value (made by thousands of people) based upon all readily-available information. Today's price may be higher than tomorrow's, but that doesn't mean today's price is not the best estimate of value today. It simply means that tomorrow's estimate is lower because new information has come to light.

The reason that you can sometimes get a bargain in real estate is that the real estate market is far less efficient than the stock (and bond) market.
Last edited by Call_Me_Op on Tue Sep 04, 2018 8:03 am, edited 1 time in total.
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Re: Why are you not compensated for taking unsystematic risk?

Post by bgf » Tue Sep 04, 2018 8:02 am

steve321 wrote:
Tue Sep 04, 2018 7:42 am
Call_Me_Op wrote:
Tue Sep 04, 2018 7:34 am
Tamalak wrote:
Tue Sep 04, 2018 7:09 am
You are rewarded for taking unsystemic risk, if you have good reason to believe that the individual stock you're buying is too cheap.
Just because you believe the stock you're buying is too cheap does not mean it is. The fact that the securities are believed to be cheap by some people and expensive by other people is why the price goes up and down. This does not change the fact that on average, you are not rewarded for taking unsystematic (company-specific) risk.
this seems to imply that the consensus is better than the informed opinion of some people. Surely in other areas of life this is not the case: if you want to build an airplane you don't go asking everyone for an answer to the math problems you need to solve and base your answer on the consensus, but you rely on those who know about fluid dynamics.
So why should the consensus in the markets be necessarily right? At least in real estate it's possible to make good bargains if you are smart enough, so I guess it should be possible in stocks too, perhaps particularly in small stocks.
markets are a good way at reaching accurate estimates, but they are not perfect. this is immediately apparently. stock prices would not fluctuate to the extent they do if markets were perfect at valuing companies. still, markets are quite good. tough to beat, though not impossible. its just a difficult game to play, and you are best served only playing the game if you have an articulable, quantifiable, and, most importantly, practical edge. there are individuals and firms that have this ability. most don't.

as for small stocks, investors generally underestimate the number of people "following" small caps, even very small ones. there is a lot of information out there on every stock listed. point being, you do not have an edge simply because you decided to stick to small caps and microcaps. they are still analyzed, followed closely, and have institutional investment.

from my perspective, you diversify your holdings more to insure that you are invested in the best long term companies (these generate huge long term return and create massive amounts of wealth), and less to avoid the companies that go bankrupt or otherwise perform poorly. in that sense, people often get the benefit of diversification backwards. they point to Enron or GE rather than to Amazon and Apple.
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Re: Why are you not compensated for taking unsystematic risk?

Post by nisiprius » Tue Sep 04, 2018 8:15 am

steve321 wrote:
Tue Sep 04, 2018 7:42 am
...this seems to imply that the consensus is better than the informed opinion of some people. Surely in other areas of life this is not the case...
That's absolutely right. Investing is different from other areas of life.

And the whole issue is do I really believe my opinion on the price of a stock is better than the consensus, and if so, why.

Everyone knows that Amazon and Apple are good companies. Furthermore, the analysts who are reading the balance sheets and all that stuff probably do own iPhones and order stuff from Amazon, so they also have the everyday consumer knowledge.

Whether you are right or wrong, if you want to pick individual stocks, you need to have a pretty good answer to the question "why is my opinion of the value of the stock different from the consensus." And, by the way, it really needs to be your own personal answer, based on your own personal poking around--not something you read or heard from someone else, "Fellows, I'm not kidding. Listen, I work for Imbray and I know. You know what's behind these stocks? Well, I'll tell you. All, or nearly all, the public utilities of the Middle West and the brain of Solomon Imbray."*

(*Quotation from a novel set in the 1930s. Studs Lonigan puts all his savings into stock suggested by a friend. It doesn't turn out well.)
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Re: Why are you not compensated for taking unsystematic risk?

Post by steve321 » Tue Sep 04, 2018 8:18 am

bgf wrote:
Tue Sep 04, 2018 8:02 am


markets are a good way at reaching accurate estimates, but they are not perfect. this is immediately apparently. stock prices would not fluctuate to the extent they do if markets were perfect at valuing companies.
that's right, sometimes I've seen a share price change by a few percent (while the market did not change much overall), so I tried to google the company name to see if any information had just come out to justify that change but there was nothing new. I get the impression prices just fluctuate quite a bit for no reason. Particularly for less liquid stocks.
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Re: Why are you not compensated for taking unsystematic risk?

Post by Call_Me_Op » Tue Sep 04, 2018 8:29 am

nisiprius wrote:
Tue Sep 04, 2018 8:15 am
steve321 wrote:
Tue Sep 04, 2018 7:42 am
...this seems to imply that the consensus is better than the informed opinion of some people. Surely in other areas of life this is not the case...
That's absolutely right. Investing is different from other areas of life.

And the whole issue is do I really believe my opinion on the price of a stock is better than the consensus, and if so, why.

Everyone knows that Amazon and Apple are good companies. Furthermore, the analysts who are reading the balance sheets and all that stuff probably do own iPhones and order stuff from Amazon, so they also have the everyday consumer knowledge.

Whether you are right or wrong, if you want to pick individual stocks, you need to have a pretty good answer to the question "why is my opinion of the value of the stock different from the consensus." And, by the way, it really needs to be your own personal answer, based on your own personal poking around--not something you read or heard from someone else, "Fellows, I'm not kidding. Listen, I work for Imbray and I know. You know what's behind these stocks? Well, I'll tell you. All, or nearly all, the public utilities of the Middle West and the brain of Solomon Imbray."*

(*Quotation from a novel set in the 1930s. Studs Lonigan puts all his savings into stock suggested by a friend. It doesn't turn out well.)
Nisi,

Thanks for making my point in a way that is clearer than I could make it.
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Re: Why are you not compensated for taking unsystematic risk?

Post by cjking » Tue Sep 04, 2018 8:45 am

steve321 wrote:
Tue Sep 04, 2018 7:42 am
this seems to imply that the consensus is better than the informed opinion of some people.
Under certain conditions, the average of a crowd of independent expert's opinions is likely to be a better predictor than using any individual opinion. (That the opinions be independent is one of the conditions.)

There is a a book called "the wisdom of crowds" about this.

I believe the example where this was first noticed was at cattle fair, where a prize was on offer to who could most accurately guess the weight of meat to be generated by looking at the live animal about to be slaughtered. When a scientist reviewed the data afterwards, he found that taking an average of the guesses gave a more accurate prediction than using any individual guesses

I think the US navy also used a similar procedure to locate a sunken ship/submarine, took the average of several experts guesses to come up with a specific location none of them had chosen, and consequently found what they are looking for.

I think the explanation is something like this: imagine every expert's guess can be divided into two parts, a correct value plus an error, which can be positive or negative. So if the correct (but unknown) value is 1000, but one expert has guessed 950 and the other 1050, their guesses are expressed as 1000 - 50 and 1000 + 50. Now when you average them, the errors cancel each other out, and the bit they have in common, the true value, emerges from the randomness.

https://en.wikipedia.org/wiki/The_Wisdom_of_Crowds

The opening anecdote relates Francis Galton's surprise that the crowd at a county fair accurately guessed the weight of an ox when their individual guesses were averaged (the average was closer to the ox's true butchered weight than the estimates of most crowd members)

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Re: Why are you not compensated for taking unsystematic risk?

Post by Call_Me_Op » Tue Sep 04, 2018 8:52 am

cjking wrote:
Tue Sep 04, 2018 8:45 am
steve321 wrote:
Tue Sep 04, 2018 7:42 am
this seems to imply that the consensus is better than the informed opinion of some people.
Under certain conditions, the average of a crowd of independent expert's opinions is likely to be a better predictor than using any individual opinion. (That the opinions be independent is one of the conditions.)

There is a a book called "the wisdom of crowds" about this.

I believe the example where this was first noticed was at cattle fair, where a prize was on offer to who could most accurately guess the weight of meat to be generated by looking at the live animal about to be slaughtered. When a scientist reviewed the data afterwards, he found that taking an average of the guesses gave a more accurate prediction than using any individual guesses

I think the US navy also used a similar procedure to locate a sunken ship/submarine, took the average of several experts guesses to come up with a specific location none of them had chosen, and consequently found what they are looking for.

I think the explanation is something like this: imagine every expert's guess can be divided into two parts, a correct value plus an error, which can be positive or negative. So if the correct (but unknown) value is 1000, but one expert has guessed 950 and the other 1050, their guesses are expressed as 1000 - 50 and 1000 + 50. Now when you average them, the errors cancel each other out, and the bit they have in common, the true value, emerges from the randomness.

https://en.wikipedia.org/wiki/The_Wisdom_of_Crowds

The opening anecdote relates Francis Galton's surprise that the crowd at a county fair accurately guessed the weight of an ox when their individual guesses were averaged (the average was closer to the ox's true butchered weight than the estimates of most crowd members)
More generally, instead of the errors cancelling, they would add in quadrature because they are uncorrelated. Thus, the error in the decision would decrease with the square-root of the number of independent estimates.
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Re: Why are you not compensated for taking unsystematic risk?

Post by dharrythomas » Tue Sep 04, 2018 8:53 am

The real reason is that unsystematic risk is a zero sum game and in a zero sum game the return for all players is ZERO. The same amount of :moneybag will be lost as won.

An individual may come out ahead by taking uncompensated risk, but the system as a whole can only break even--somebody has to be on the other side of the bet so as a whole there is no premium for unsystematic risk.

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Re: Why are you not compensated for taking unsystematic risk?

Post by steve321 » Tue Sep 04, 2018 9:00 am

cjking wrote:
Tue Sep 04, 2018 8:45 am
steve321 wrote:
Tue Sep 04, 2018 7:42 am
this seems to imply that the consensus is better than the informed opinion of some people.
Under certain conditions, the average of a crowd of independent expert's opinions is likely to be a better predictor than using any individual opinion. (That the opinions be independent is one of the conditions.)

There is a a book called "the wisdom of crowds" about this.

I believe the example where this was first noticed was at cattle fair, where a prize was on offer to who could most accurately guess the weight of meat to be generated by looking at the live animal about to be slaughtered. When a scientist reviewed the data afterwards, he found that taking an average of the guesses gave a more accurate prediction than using any individual guesses

I think the US navy also used a similar procedure to locate a sunken ship/submarine, took the average of several experts guesses to come up with a specific location none of them had chosen, and consequently found what they are looking for.

I think the explanation is something like this: imagine every expert's guess can be divided into two parts, a correct value plus an error, which can be positive or negative. So if the correct (but unknown) value is 1000, but one expert has guessed 950 and the other 1050, their guesses are expressed as 1000 - 50 and 1000 + 50. Now when you average them, the errors cancel each other out, and the bit they have in common, the true value, emerges from the randomness.

https://en.wikipedia.org/wiki/The_Wisdom_of_Crowds

The opening anecdote relates Francis Galton's surprise that the crowd at a county fair accurately guessed the weight of an ox when their individual guesses were averaged (the average was closer to the ox's true butchered weight than the estimates of most crowd members)
That's fascinating thanks; I now remember watching a video in which the guy who put forward the Magic formula explained the stock market by getting people to estimate the number of coloured balls in a container. The average of the guesses was quite accurate apparently.
I like your explanation and the idea that the opinions have to be independent. Otherwise you get people jumping on a bandwagon and bubbles I guess.
Also, the idea of independent opinions might imply that this method might not apply to things like bitcoin, because I get the impression that the only reason people value it is that they see others paying a high price for it. But an independent valuation is probably impossible for bitcoin (unlike for stocks).
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Re: Why are you not compensated for taking unsystematic risk?

Post by aristotelian » Tue Sep 04, 2018 9:15 am

steve321 wrote:
Tue Sep 04, 2018 6:26 am
That's a good explanation, thank you for taking the time, I appreciate it. So basically using your example someone buying only one stock might end up making a lot more profit (like if I buy one box for 100k$ and it turns out to be the one worth 200K$) but may also have a much bigger loss (if instead it turns out to be worth nothing). So yes one might be shooting for the stars and end up in the gutter.
Wisest way is to diversify, now I see that; I am still not sure whether you need to get as many as 3,564 stocks or whatever (also because if you index most the contribution to your fund actually comes from the big stocks) but if you can get them cheap in an ETF I guess why not?
Basically one problem I have with indexing is that I personally don't find many boring Uk companies attractive compared to Amazon, it just seems a waste of money to invest in them. But then I guess the Boglehead answer is that the market has priced all those companies efficiently to reflect their prospects, so it would be arrogant to think that I know better.
I think you are right to an extent. After about 100 or so stocks diversified across sectors, the reduction in risk for additional diversification approaches zero. Many threads have discussed the very close correlation between S&P500 and total US market, for example. The thing is, index funds are so cheap these days - literally 0% expense ratio now - there is no reason not to maximize diversification, particularly in a nontaxable account.

(In a taxable account, there may be some justification in that individual stocks allow for greater opportunity to harvest losses and gains in the most efficient manner, which you cannot do with indices. Note that the justification has nothing to do with expected returns. In the past trading fees to manage individual stocks would have been a prohibitive concern, but that is starting to change now with JP Morgan YouInvest, Robinhood etc).
Last edited by aristotelian on Tue Sep 04, 2018 9:21 am, edited 2 times in total.

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Re: Why are you not compensated for taking unsystematic risk?

Post by cjking » Tue Sep 04, 2018 9:20 am

I don't think the difference between bitcoin and stocks is clear-cut, stock-markets also have irrational bubbles. I think usually most markets are close enough to the required conditions for the wisdom of crowds to work, but when a mania takes hold independence breaks down, then after the bubble bursts it returns again. The problem with bitcoin is not the product, or even the specific individuals, but the fact the individuals are (at a particular time) in the grip of an investment mania. (The title "the wisdom of crowds" was presumably a play on the even older book about investment manias, the "the madness of crowds".)

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Re: Why are you not compensated for taking unsystematic risk?

Post by steve321 » Tue Sep 04, 2018 9:26 am

cjking wrote:
Tue Sep 04, 2018 9:20 am
I don't think the difference between bitcoin and stocks is clear-cut, stock-markets also have irrational bubbles. I think usually most markets are close enough to the required conditions for the wisdom of crowds to work, but when a mania takes hold independence breaks down, then after the bubble bursts it returns again. The problem with bitcoin is not the product, or even the specific individuals, but the fact the individuals are (at a particular time) in the grip of an investment mania. (The title "the wisdom of crowds" was presumably a play on the even older book about investment manias, the "the madness of crowds".)
yes, I heard of that book. But on the subject of bitcoin - though I am going a bit off topic - my thought was that you don't really have the elements to value it independently, do you? It's not like stocks that correspond to a firm which has earnings E, so you decide on a price P that you are prepared to pay (and like you say that price can get irrational). With bitcoin there's inherently no rational or independent way of determining the price, except from the fact that you hope other people will buy it from you at a higher price. At least that's my understanding of it.
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Re: Why are you not compensated for taking unsystematic risk?

Post by JBTX » Tue Sep 04, 2018 9:49 am

steve321 wrote:
Tue Sep 04, 2018 2:16 am
The following piece of advice has been given to me, on the question of whether buying individual stocks makes sense:
The main thing is that you would be taking unsystematic risk. Because unsystematic risk is diversifiable, you are not compensated for taking this risk.
I found this quote very interesting (and a bit puzzling) and I thought this question deserves consideration from a theoretical perspective: can anyone explain why investors are compensated for taking systematic risk (I take it to mean the risk associated with the whole market(?)), but not unsystematic risk (I take it to mean risk of individual stocks)?
My amateur take on this is that diversification by definition and intuitively will typically lower risk, and it is mathematically impossible for an individually held individual stock to have a higher level of return than its part of a diversified portfolio.

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Re: Why are you not compensated for taking unsystematic risk?

Post by Theoretical » Tue Sep 04, 2018 10:16 am

I think the individual stock investor is compensated for that risk by having proxy votes and no overlay/management fee. However, this risk cannot be fully compensated because the risk of all stocks or all stocks in most developed and even emerging countries going to 0 is present but has a practical likelihood of 0% to the extent someone actually cares. If Mad Max happens, no one really cares what your Nike stock or VTI is worth because you’re either dead or trying to survive.

The difference with an individual stock is that while it has unlimited upside, it also has far more reasons beyond Mad Max scenarios that could cause it to go to 0 or some other permanent loss.

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Re: Why are you not compensated for taking unsystematic risk?

Post by acegolfer » Tue Sep 04, 2018 10:24 am

steve321 wrote:
Tue Sep 04, 2018 2:16 am
The following piece of advice has been given to me, on the question of whether buying individual stocks makes sense:
The main thing is that you would be taking unsystematic risk. Because unsystematic risk is diversifiable, you are not compensated for taking this risk.
I found this quote very interesting (and a bit puzzling) and I thought this question deserves consideration from a theoretical perspective: can anyone explain why investors are compensated for taking systematic risk (I take it to mean the risk associated with the whole market(?)), but not unsystematic risk (I take it to mean risk of individual stocks)?
I can provide a brief theoretical development that led to the conclusion that unsystematic risk are not compensated.

Textbooks usually start with explaining the difference between systematic vs unsystematic (=diversifiable) risks. However, in fact, this is the result of the theory academia developed over time.

Here's how the asset pricing theory developed over time. It doesn't really depend on diversification. (I'll skip all the assumptions and proofs)
1. Reward is measured by expected return and risk is measured by standard deviation.
2. Drew efficient frontier in mean-variance diagram. Tried to explain expected return by standard deviation (=total risk). We failed.
3. Created capital market line (CML) by introducing risk-free asset. CML implies all investors will hold the same risky-asset portfolio. Conclusion: market portfolio is on mean-variance efficient frontier.
4. Since MKT is on efficient frontier, it's an asset pricing factor. IOW, we can express expected excess return of any stock by beta * expected excess market return. E(Ri)-Rf = beta_i * ( E(Rm) - Rf )
5. variance(return) = beta^2 * variance of market + variance of individual error. The first part is referred as systematic risk, which includes beta (the part that affects the expected return in #4). OTOH, the latter part is referred as idiosyncratic risk, which is irrelevant to the expected return of a stock.

(This is the simplest I can verbally explain without getting into details. It takes about 2 weeks to learn all these with mathematical proofs at a doctoral level course.)

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Re: Why are you not compensated for taking unsystematic risk?

Post by bottlecap » Tue Sep 04, 2018 10:29 am

The problem is that taking unsystematic risk does not increase your expected return. So why take it if you are not being compensated commensurately? From that standpoint, you are taking additional risk without being compensated extra for it. Hence, uncompensated.

If you posited the reverse of your question, "Why doesn't investing in one stock increase your expected return?", then the answers you can think of give you an idea of why people say that unsystematic risk is uncompensated risk.

JT

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Re: Why are you not compensated for taking unsystematic risk?

Post by Phineas J. Whoopee » Tue Sep 04, 2018 10:38 am

JBTX wrote:
Tue Sep 04, 2018 9:49 am
...
My amateur take on this is that diversification by definition and intuitively will typically lower risk, and it is mathematically impossible for an individually held individual stock to have a higher level of return than its part of a diversified portfolio.
Hi JBTX. Presumably you misspoke.

It is all but certain any individual stock will have a different return than the market as a whole, either higher or lower, over a defined time period.

PJW

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Re: Why are you not compensated for taking unsystematic risk?

Post by steve321 » Tue Sep 04, 2018 10:49 am

acegolfer wrote:
Tue Sep 04, 2018 10:24 am
IOW, we can express expected excess return of any stock by beta * expected excess market return. E(Ri)-Rf = beta_i * ( E(Rm) - Rf )
But then my understanding is that besides beta, factors like size and value or momentum are also important: how do they fit in?

Also, people talk of low volatility (so presumably low beta) as a factor of outperformance (I was recently talked into buying a min volatility iShares ETF for Emerging Markets). How can low volatility stocks outperform, when in your equation the excess return is proportional to beta?
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Re: Why are you not compensated for taking unsystematic risk?

Post by JBTX » Tue Sep 04, 2018 10:51 am

Phineas J. Whoopee wrote:
Tue Sep 04, 2018 10:38 am
JBTX wrote:
Tue Sep 04, 2018 9:49 am
...
My amateur take on this is that diversification by definition and intuitively will typically lower risk, and it is mathematically impossible for an individually held individual stock to have a higher level of return than its part of a diversified portfolio.
Hi JBTX. Presumably you misspoke.

It is all but certain any individual stock will have a different return than the market as a whole, either higher or lower, over a defined time period.

PJW
Thus the qualifier "than its part".

If stock a earns 10% as a broad part of a 3000+ diversified portfolio, it can't earn 12% by itself.

Obviously an individual stock will have a different return than the entire market portfolio.

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Re: Why are you not compensated for taking unsystematic risk?

Post by Phineas J. Whoopee » Tue Sep 04, 2018 10:55 am

JBTX wrote:
Tue Sep 04, 2018 10:51 am
Phineas J. Whoopee wrote:
Tue Sep 04, 2018 10:38 am
JBTX wrote:
Tue Sep 04, 2018 9:49 am
...
My amateur take on this is that diversification by definition and intuitively will typically lower risk, and it is mathematically impossible for an individually held individual stock to have a higher level of return than its part of a diversified portfolio.
Hi JBTX. Presumably you misspoke.

It is all but certain any individual stock will have a different return than the market as a whole, either higher or lower, over a defined time period.

PJW
Thus the qualifier "than its part".

If stock a earns 10% as a broad part of a 3000+ diversified portfolio, it can't earn 12% by itself.

Obviously an individual stock will have a different return than the entire market portfolio.
Got it. Fair enough.

PJW

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Re: Why are you not compensated for taking unsystematic risk?

Post by Northern Flicker » Tue Sep 04, 2018 12:49 pm

steve321 wrote:
Tue Sep 04, 2018 2:16 am
The following piece of advice has been given to me, on the question of whether buying individual stocks makes sense:
The main thing is that you would be taking unsystematic risk. Because unsystematic risk is diversifiable, you are not compensated for taking this risk.
I found this quote very interesting (and a bit puzzling) and I thought this question deserves consideration from a theoretical perspective: can anyone explain why investors are compensated for taking systematic risk (I take it to mean the risk associated with the whole market(?)), but not unsystematic risk (I take it to mean risk of individual stocks)?
There are several ways to demonstrate it. The simplest argument is that when you buy or sell an individual stock, the market establishes a price you will pay or receive for it. The market has no way of knowing whether you plan to hold a concentrated position in the stock or plan to integrate the holding into a well diversified portfolio in which uncompensated risk is diversified away. And the dividends you receive will be the same either way.

Your return on an individual stock is based on the purchase price, selling price, dividends received and transaction costs. Since none of these vary whether or not you integrate the stock into a diversified portfolio, your return is the same either way. Hence, there is no additional return for holding and taking the risk of a concentrated position in the stock.
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Re: Why are you not compensated for taking unsystematic risk?

Post by acegolfer » Tue Sep 04, 2018 12:51 pm

steve321 wrote:
Tue Sep 04, 2018 10:49 am
acegolfer wrote:
Tue Sep 04, 2018 10:24 am
IOW, we can express expected excess return of any stock by beta * expected excess market return. E(Ri)-Rf = beta_i * ( E(Rm) - Rf )
But then my understanding is that besides beta, factors like size and value or momentum are also important: how do they fit in?

Also, people talk of low volatility (so presumably low beta) as a factor of outperformance (I was recently talked into buying a min volatility iShares ETF for Emerging Markets). How can low volatility stocks outperform, when in your equation the excess return is proportional to beta?
1. In 70's, we found that the average returns of small companies were higher than the expected returns indicated by CAPM. This was an empirical evidence that MKT is not on M-V efficient frontier and CAPM failed. We had to introduce more factors to explain the cross section of average returns.

2. I haven't heard about your 2nd paragraph. And low volatility and low beta are not the same. A stock can have a low beta but a high standard deviation. Or perhaps, we have different definition of volatility. I don't consider beta as a measure of volatility.

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Re: Why are you not compensated for taking unsystematic risk?

Post by Nate79 » Tue Sep 04, 2018 1:31 pm

OP, a good read can be the story of GTAT. As far as I can tell the original thread on the investment into this company is gone. The links appear to be dead but the below two threads, one by WCI the other on BH explains the background. The original investment thread though was so interesting. The investors posting in that thread were really deep diving into the company, learning every single detail and based on where they though the company was going sunk significant investments into it. They were so sure of themselves. They explained in great detail why the company was going to have a big increase.

In the end they went bankrupt and what was shooting sky high went splat. Even when the bankruptcy was filed the investors still didn't believe it because they were so sure of their research.


https://www.whitecoatinvestor.com/putti ... ne-basket/

viewtopic.php?f=10&t=148446

This is an extreme cautionary tale that you may think all you want that you can do research and tell the direction of a company but there is still a lot of risk and companies can go to zero.

Here is another great BH thread on individual stocks that have gone to zero:
viewtopic.php?t=236214

The list is long.......

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Re: Why are you not compensated for taking unsystematic risk?

Post by steve321 » Tue Sep 04, 2018 1:38 pm

acegolfer wrote:
Tue Sep 04, 2018 12:51 pm
And low volatility and low beta are not the same. A stock can have a low beta but a high standard deviation. Or perhaps, we have different definition of volatility. I don't consider beta as a measure of volatility.
Well, from Investopedia
A security's beta is calculated by dividing the covariance the security's returns and the benchmark's returns by the variance of the benchmark's returns over a specified period.
So beta measures the volatility of a stock price relative to the market (e.g. beta<1 means that it is less volatile than the market and beta>1 that it is more volatile)
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Re: Why are you not compensated for taking unsystematic risk?

Post by acegolfer » Tue Sep 04, 2018 2:28 pm

steve321 wrote:
Tue Sep 04, 2018 1:38 pm
So beta measures the volatility of a stock price relative to the market (e.g. beta<1 means that it is less volatile than the market and beta>1 that it is more volatile)
Apparently, we have different definitions for volatility, which is fine. You described volatility as systematic risk. I consider volatility as total risk (=systematic + unsystematic risk), which is measured by stdev.
Also, people talk of low volatility (so presumably low beta) as a factor of outperformance (I was recently talked into buying a min volatility iShares ETF for Emerging Markets). How can low volatility stocks outperform, when in your equation the excess return is proportional to beta?
I haven't seen anyone saying low beta as a factor of outperformance. Holding all else equal, low beta stocks should have lower expected return.

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Re: Why are you not compensated for taking unsystematic risk?

Post by steve321 » Tue Sep 04, 2018 2:43 pm

acegolfer wrote:
Tue Sep 04, 2018 2:28 pm


I haven't seen anyone saying low beta as a factor of outperformance. Holding all else equal, low beta stocks should have lower expected return.
you can check a number of blogs and articles, such as this
https://www.etf.com/sections/index-inve ... -anomaly-0
or this one more technical and involving leverage to exploit the anomaly
http://pages.stern.nyu.edu/~lpederse/pa ... stBeta.pdf
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Re: Why are you not compensated for taking unsystematic risk?

Post by JoMoney » Tue Sep 04, 2018 2:45 pm

steve321 wrote:
Tue Sep 04, 2018 2:43 pm
acegolfer wrote:
Tue Sep 04, 2018 2:28 pm


I haven't seen anyone saying low beta as a factor of outperformance. Holding all else equal, low beta stocks should have lower expected return.
you can check a number of blogs and articles, such as this
https://www.etf.com/sections/index-inve ... -anomaly-0
or this one more technical and involving leverage to exploit the anomaly
http://pages.stern.nyu.edu/~lpederse/pa ... stBeta.pdf
The failure of 'beta' as the measure of risk to fully describe returns is what lead to other "risk factors" like size and value factors to measure exposure to those risks as well.
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Re: Why are you not compensated for taking unsystematic risk?

Post by acegolfer » Tue Sep 04, 2018 3:18 pm

steve321 wrote:
Tue Sep 04, 2018 2:43 pm
you can check a number of blogs and articles, such as this
https://www.etf.com/sections/index-inve ... -anomaly-0
or this one more technical and involving leverage to exploit the anomaly
http://pages.stern.nyu.edu/~lpederse/pa ... stBeta.pdf
Just read those 2 articles. If you conclude low beta is a factor of outperformance, I'd argue you are taking it out of context. The correct way to interpret is low beta stocks provided higher average return than what CAPM expected.

What we found in the last 50 years is that beta alone can't explain the cross section of average returns. To explain E(Ri) better, we introduced 2-4 more systematic risk factors. To answer OP's question, even with the multi-factor model, the idiosyncratic risk is not compensated.

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Re: Why are you not compensated for taking unsystematic risk?

Post by ThrustVectoring » Tue Sep 04, 2018 4:23 pm

acegolfer wrote:
Tue Sep 04, 2018 2:28 pm
I haven't seen anyone saying low beta as a factor of outperformance. Holding all else equal, low beta stocks should have lower expected return.
Low beta have lower expected returns, but even lower risks. This is because capital and leverage constrained investors need absolute return, not risk-adjusted, so they overpay for higher-risk assets in lieu of levering up lower-risk assets. Bet-against-beta explains a good chunk of Buffett's success: he'd often buy up relatively boring companies that other investors were less interested in, and then juice the returns through the cheap debt financing he had access to.

The bet-against-beta factor is far more obvious and relevant in bond markets, where there's a much better signal-to-noise ratio. In the stock market, you're mostly guessing that boring stocks are going to have the behavior you want going forward, and it's generally just far messier. Treasury futures OTOH have an extraordinarily liquid market and are very well understood. Duration is the equivalent to beta here, and the implementation details are basically taking on a reasonable amount of leverage on 2-year treasury futures and optionally hedging your interest rate risk through shorting the 30 year or 30 year ultra contract.
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Re: Why are you not compensated for taking unsystematic risk?

Post by Northern Flicker » Tue Sep 04, 2018 11:06 pm

can anyone explain why investors are compensated for taking systematic risk
Because the risk cannot be diversified away, the market demands that a suitable risk premium be discounted into a stock based on its exposure to this undiversifiable risk.
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