# Risk And Return

One of the most fundamental concepts in finance is that risk and return are correlated. We touched on this a tiny bit in one of the early MBA Mondays posts. But I'd like to dig a bit deeper on this concept today.

Here's a chart I found on the Internet (where else?) that shows a bunch of portfolios of financial assets plotted on chart.

As you can see portfolio 4 has the lowest risk and the lowest return. Portfolio 10 has the highest risk and the highest return. While you can't draw a straight line between all of them, meaning that risk and return aren't always perfectly correlated, you can see that there is a direct relationship between risk and return.

This makes sense if you think about it. We don't expect to make much interest on bank deposits that are guaranteed by the federal government (although maybe we should). But we do expect to make a big return on an investment in a startup company.

There is a formula well known to finance students called the Capital Asset Pricing Model which describes the relationship between risk and return. This model says that:

Expected Return On An Asset = Risk Free Rate + Beta (Expect Market Return – Risk Free Rate)

I don't want to dig too deeply into this model, click on the link on the model above to go to WIkipedia for a deeper dive. But I do want to talk a bit about the formula to extract the notion of risk and return.

The formula says your expected return on an asset (bank account, bond, stock, venture deal, real estate deal) is equal to the risk free rate (treasury bills or an insured bank account) plus a coefficient (called Beta) times the "market premium." Basically the formula says the more risk you take (Beta) the more return you will get.

You may have heard this term Beta in popular speak. "That's a high beta stock" is a common refrain. It means that it is a risky asset. Beta (another Wikipedia link) is a quantitative measure of risk. It's formula is:

Covariance (asset, portfolio)/Variance (portfolio)

I've probably lost most everyone who isn't a math/stats geek by now. In an attempt to get you all back, Beta is a measure of volatility. The more an asset's returns move around in ways that are driven by the underlying market (the covariance), the higher the Beta and the risk will be.

So, when you think about returns, think about them in the context of risk. You can get to higher returns by taking on higher risk. And to some degree we should. It doesn't make sense for a young person to put all of their savings in a bank account unless they will need them soon. Because they can make a greater return by putting them into something where there is more risk. But we must also understand that risk means risk of loss, either partial or in some cases total loss.

Markets get out of whack sometimes. The tech stock market got out of whack in the late 90s. The subprime mortgage market got out of whack in the middle of the last decade. When you invest in those kinds of markets, you are taking on a lot of risk. Markets that go up will at some point come down. So if you go out on the risk/reward curve in search of higher returns, understand that you are taking on more risk. That means risk of loss.

Next week we will talk about diversification. One of my favorite risk mitigation strategies.

1. Julien

I find it interesting to see that there are different kind of risks : company risks, market risks, and even “systemic risks”.When the economy goes well, all the risks are in the companies, which, in way is “right”. The only thing that matters is how the team executes. Unfortunately, there are times where the market risk (housing crash!) or the systemic risk is just too high for good operators to see the expected returns.I would love to hear about the current beta in the venture ecosystem. My bet is that it’s always very high, which induces stress for the VCs themselves, that they tend to transfer down to the startups in which they invest.

1. fredwilson

ouchrisk in VC is high but that is to be expectedhow you identify, manage, and mitigate risk is the keyand as you say, you need to do that without dumping all of the stress on the founding teams you back

1. azeemazhar

beta is startup companies is high — or rather the risk is high as they tend to be super small caps relative to other assets.i’ve often wondered whether the risk is necessarily much higher than many internal projects run by large companies (like M&A, joint ventures or even large IT projects). (see this : http://www.it-cortex.com/St… )one of the key differences seems to be that extent to which the risk is held by single individuals–you can blow a £5bn IT project and not lose your job. You can blow £500k on a boot-strapped startup and lose your house.and that in itself leads to a principal-agent problem in large companies–because the losses from failure do not accrue to the individuals but rather to a widely-dispersed range of shareholders–people end up taking risks that they shoulnd’t. (But disguise them as low risk opportunities).If 61% of large IT projects within big companies fail, that seems to be higher than the out-and-out failure rate within venture. (where failure is defined as 1x or less)

2. K H

Fred, you may want to mention that what you drew out in your graph can also refer to the efficient frontier. The investor’s tangency point, its highest risk to reward ratio, is the slope, which is called the Sharpe ratio, which measures risk per expected return: (expected risk of market – Risk free) / std deviationThe SML (or CAL), which is the slope, can be different for each investor, because each investor has different risk/reward profiles.However, the CML, which has 5 underlying assumptions, tates that all investors have the same risk/return profile and they all lie on the efficient frontier. There is a point where adding more risk, results in diminishing marginal returns, therefore there is an ideal point, which is above the mininum variance point on the graph (lowest risk).

1. fredwilson

i was tempted to get into a discussion of the efficient frontier but i think that should wait for another postgreat topic. thanks for bring it up

1. K H

Fred, Have you ever looked at the Venture Capital section of CFA Level 2 curriculum? I wonder how relevant it is to today’s world.

2. Mark Essel

Appreciate you breaking it up into bite sized morsels.

3. Bala

I take a contrarian view on this, risk on a VC is actually much lower than the risk in the general market… we don’t know how to measure risk in the general market in a startup you exactly where the risks are… it is always in the Team and Execution. I think VC’s generally add in more risk by enforcing some time limit on the investment (I am not meaning you do Fred… I love your definition of Slow Capital, i try to follow it).Regards,Bala

2. azeemazhar

Hey Fred,The idea that risk and return are correlated is a powerful one. I do wonder about the applicability of CAPM–other than being a nice theoretical model. First of all there are the Fama-French extensions to it (which essentially say that ‘beta’ isn’t a great explanatary variable compared to capital efficiency or market cap). The second is the nature of returns and whether they truly follow a simple Gaussian distribution–or perhaps in understanding what really is the asset you are holding.Is being an entrepreneur in a tech company, really similar to being an exec it a BlueChip megacorp but with more volatility? Or is being an entrepreneur in a tech company more like holding a European-style call option which is priced deeply out of the money? Essentially, the call option is either worth nothing or it’s worth a lot; and there isn’t much in between.And if the latter–and given as an entrepreneur you can only hold one of these at a time–how do you go about thinking about your risk and return?

1. fredwilson

i agree that CAPM has its limitationsbut in terms of laying out that risk and return have a direct relationship with each other, it’s a powerful model

3. Morten Josefsen

Another great post!I guess there is no use in splitting too many hairs over this, but I think some might be a bit confused about “The more an asset’s returns move around in ways that aren’t driven by the underlying market (the covariance), the higher the Beta and the risk will be.”Covariance/beta is, the way I see it, the opposite! If a stock moves a lot driven by the underlying market (car manufacturers, construction companies), then it has high covariance/beta, while if it moves a lot randomly, or based on its own fundamentals (agriculture, utilities), it has low covariance/beta.

1. fredwilson

right, i will fix that morten

4. kidmercury

there is no such thing as risk-free, especially if treasury bond rates are what is being used to determine the alleged “risk-free” rate. CAPM is thus useless, a disgrace. an embarrassment.out in kook world, gold is a safe haven, because gold is real money. thus rate of return relative to gold can help identify true risk. this is becoming more meaningful as fiat currencies of the world collapse, as they always have, throughout thousands of years of human history.to make matters even more embarrassing, the FDIC is bankrupt. http ://www. garynorth. com/public/6025.cfmso, dollars in a US bank is not risk-free either, as bank failures will be paid for via currency debasement.

1. fredwilson

How did I know you’d have this take?I even acknowledged it a bit in my post when I noted that federally insured bank deposits might not be risk freeThat said, to call capm a disgrace is a bit harsh in my view

1. kidmercury

not just a disgrace, boss. an embarrassment.

1. K H

And it is with that attitude, and lack of financial knowledge that you sit on AVC writing up comments, while many people make alot of money using CAPM as a fundamental basis for their portfolio management techniques.And FYI, Capm is not ANY gov’t bond. The capm in Zimbabwe is not the Zimbabwe gov’t bonds. To go international, you get into ICAMP, or Extended CAPM. And it is not the tell all either. It is a fundamental starting point, that has much significance in the financial world.

1. akharris

To be fair, the fact that a lot of people use CAPM as a fundamental basis of moneymaking portfolios is not a proof that CAPM is the right way to look at things. Either it holds from a logical standpoint, or it does not. There are a lot of people who make money of rank speculation, and there are a lot of people who lose money with CAPM styled portfolios.Looking forward to the chat on diversification, though, it should nicely echo some of what we were all discussing last week re: real estate and gold.

2. kidmercury

1. many people who use CAPM also make money. but that does not mean mean CAPM causes profitable analysis. correlation does not lead to causality.2. i don’t care what bond CAPM represents. CAPM presupposes that there is such a thing as a risk-free asset. there is no such thing. to assume that a government bond is risk-free is especially comical.3. CAPM is a fundamental starting point in the financial world. is this the same financial world that was completely blindsided by the allegedly unforeseeable crisis of 2008? funny, because myself and others who adhere to kookonomics saw it coming a mile away. we even tried to warn those who adhere to CAPM. they disregarded us.point #3 is especially crucial. it explains why CAPM is so unbelievably embarrassing.damn.

3. K H

The relation between CAPM and the CDO crisis of 2008 are very far apart. So I would disagree that CAPM had much to do with the crisis. That was the investment banks just getting way too creative for their own good.

4. kidmercury

the 2008 crisis, which is still going on, is a global sovereign debt crisis at its core. the governments of the world have promised more debt than they can ever repay. this is in part because everyone thinks their bonds are risk-free, and so they keep buying them.

5. Mark Essel

The debts are either repaid, or we require wheel barrows of currency to buy bread.

6. Dan Ramsden

To add to this, the global financial crisis has also to do with poor assessment of “risk assets” and poor portfolio strategy, both of which directly or indirectly relate back to CAPM. More precisely, to the misuse thereof.

7. sigmaalgebra

It’s CALLED a ‘risk-free asset’; for the theory to hold, you don’t have to take ‘risk-free’ literally.Gee, somewhere out there could be a star about ready to be a gamma ray burst. Or, it could be X – 1 light years away and did a gamma ray burst aimed at us X years ago. The first indication we will get will be in 1 year. If the star is in our galaxy, then the burst could blow the atmosphere off the Earth. So, ‘risk-free’ is not to be taken literally.But, slightly touch up the math and it still works.

2. David Semeria

Sovereign borrowers can’t go bust because they can always print more money and use it to pay off the debt – and in the past many of them did.Whilst the consequences of this approach are nearly always disastrous, this situation does in no way undermine the theoretical foundations of the CAPM.

1. kidmercury

CAPM defines risk-free as the rate on government bonds. this is not risk-free as in a currency crisis government bonds will be worthless due to currency debasement. CAPM is based on risk-free rate being government bonds. moreover, it implies there is a risk-free rate to begin with — that some store of wealth can in fact be risk-free. this is false and thus CAPM is a shameful disgrace.

1. David Semeria

Nope. In this context, ‘risk free’ means you’re guaranteed to get back the *nominal* amount you lent.Whilst the components making up the risk free rate are complex, the principal one captures inflation expectations for currency in which the loan made.This is why government bonds issued by countries with a bad inflation record always trade at a discount (implying a higher RFR) to those issued by countries with a good inflation history.

1. kidmercury

Rate on govt bonds is routinely below rate of price inflation — in the US it has been like this for most of the past decade. If rate of return on govt bonds is below rate of price inflation for non-financial assets, this is a loss of purchasing power, and thus not a risk-free investment.

2. JLM

Made only the more interesting by being paid off w/ inflated dollars.

3. ShanaC

Russia in LTCM? Nearly lost their currency-Or why have there been 3 different israeli currencies? Just because you can print the money, doesn’t the money holds value and it will pay off debt.

3. Dan Ramsden

Echoing this, and then some: CAPM and its component parts presuppose some degree of market efficiency, which nowadays seems increasingly a thing of the past. Between huge capital concentration and machine trading that now constitutes 70% of market volume, the idea of “the wisdom of crowds” that underlies efficient markets, is blown to bits. When the largest banks, each one, has had a winning trading day, every day, for something like two straight months, this is not an efficient market but a game that’s rigged. It isn’t that financial theory no longer applies, but Modigliani/Miller seems much less satisfactory now.

1. kidmercury

ouch. brutal truth you just dropped dan. +1.

2. andyidsinga

non sequitur: when you said Modigiani I thought of the Seinfeld mulligatawny soup :)I’m here all week.

3. Mark Essel

Dave Pinsen shed some light on this for a noob-finance guy like myself in Too Big to Fail in English. A coin that results in tails after 60 consecutive flips should result in only one conclusion, it’s far from balanced.

4. Dave Pinsen

Consider also the rise of indexing (and closet indexing). That really put a wrench in the “wisdom of crowds” works, as money managers increasingly bought stocks because everyone else owned them. So they weren’t trying to maximize their absolute returns but their relative returns, as Falkenstein elaborated on in this blog post of his, “Why envy dominates greed”.

1. Dan Ramsden

I wonder if another way of saying this is that ownership-driven enterprise, especially in finance, is being replaced by an employee culture. The bigger a firm – whether a bank, a fund, an insurance company – the more likely this becomes. Not only in finance, but finance is the subject at hand.

2. JLM

The “wisdom of crowds” is one of my favorite observations.What makes markets work is the simultaneous realization that two persons can have a complete disagreement on the proscribed action plan based upon the same information and everybody is still part of the same crowd.A bad idea, even when held by a majority, does not become a good idea.

1. Tereza

democracy at work!

5. Tereza

When people start thinking we’ve evolved “past” CAPM and are moving on to a new age of creating value, that is the first signal that things are going to nosedive.It means that shortly there’ll be a cover story in Time Magazine and your mom and dentist want in on the action.While I joke that I don’t like finance the unfettered truth is that the risk/reward tradeoff is the foundation of most if not all business decisions — operational as well as financial decisions.

1. fredwilson

remember when the “new economy” was the rage in the late 90s?

1. Tereza

exactly

6. jeremystein

“Basically the formula says the more risk you take (Beta) the more return you will get.”that statement alone is not true. because it is a pricing model, in theory, return depends on where the asset is relative to the line.its the same concept with portfolio diversification. you want to be on the efficient frontier, not above.

1. fredwilson

good point

7. Fred T

Someone once laid it out pretty clear and simple, “You don’t just take risks; you take calculated* risks.”Our friends standing on the conservative side may say that we could easily lose our money overnight with these high-volatility, “beta” investments that we are making. What they are missing is we have actually made that full extensive research and calculation of performing an exit strategy when we hit that fiscal goal or are nearing the red zone (Same is true with stocks, you have a sell point when they reach a certain level; yet keep a close eye on it) Participating in high-volatility investments is risky, but once we create the right parameters, the rewards can be well-deserving.Great way to start the week, Fred W.

8. Beth

Hi Fred,Great post! What do you think are the Top Three risks that start-up tech entrepreneurs should take to increase their return?Beth

9. Dave Pinsen

Dr. Eric Falkenstein has compellingly argued that contra CAPM, risk “is not positively related to (rational) expected returns.” Falkenstein writes that, the risk premium pervades modern economics like the luminiferous aether pervaded 19th century physics. It’s everywhere and explains everything (eg, why did markets fluctuate yesterday? The risk premium was moving!); it is also impossible to measure. One thing it certainly is not, however, is mere volatility. High beta stocks, and high volatility stocks, have lower than average returns.[…]While no one has identified this elusive factor, it’s an academic snipe hunt that has been going on for 50 years, and yet academics still believe it exists the same way any true believer knows the truth regardless of evidence. The triumph of theory over data is a powerful thing.

1. Mark Essel

I was going to say that measurements are ridden with unknown noise and biases, and no matter what theories drive volatilities they are merely estimates. I think you did a better job with the quote Dave.

1. Dave Pinsen

Mark,Falkenstein’s point is that the data essentially refutes theory. The theory suggests, for example, that you should get higher returns by investing in more volatile stocks, but as the study Falkenstein links to says, empirically, the opposite is the case. By way of elaboration, here is Falkenstein quoting Jeremey Grantham:In fact, Quality stocks have outperformed the market since 1965 (when our quality data begins) … On noticing this outperformance, embarrassingly late in my opinion, Fama and French adopted a circular argument rather typical of ﬁnance academics in the 1970 to 2000 era: the market is efﬁcient; P/B and small cap outperform, ergo they must be risk factors. That the result in this case happens to get to the right result is luck. The real behavioral market is perfectly happy not rewarding “risk” when it feels like it, as is shown by the 70-year underperformance of high beta stocks. But this time it worked. Price-to-book, despite its low beta, is a risk factor because of its low fundamental quality and its vulnerability to failure in a depression. This is true with small cap as well. But what about “Quality?” This factor has outperformed forever. (The S&P had a High Grade Index that started in 1925 and handsomely outperformed the S&P 500 to the end of 1965 when our data starts.) Since the market is efﬁcient, to Fama and French quality must be a risk factor! So, by protecting you in the 1929 Crash and in 2008, and by having a low beta for that matter, Quality as represented by Coca-Cola and Johnson & Johnson must be a hidden risk factor. Oh, I know: “The real world is merely an inconvenient special case!”______________________________

1. Elia Freedman

I am late to the party but this comment thread keeps using the word “should” when it comes to investments with higher betas. I think the word you actually want is “potential”, as in investments with higher betas have the potential for higher returns. It doesn’t mean they do in reality — as one of you pointed out and as Fred pointed out higher risk investments fail more often by nature.

2. Joe Charakupa

Dave, maybe I’m missing something here but I don’t see the point of this research because it should be obvious that “High beta stocks, and high volatility stocks, have lower than average returns.” That is why they are risky surely?What Fred should have done is to provide a caveat for his statement “Basically the formula says the more risk you take (Beta) the more return you will get.” That statement is only true for SUCCESSFUL investments. Of course how we qualify success and by extension compare the risk-factor of each investment is another issue.Fred did lose me a bit on the maths but I’d say an analogy is that in baseball, swinging for a home run is infinitely more risky than just trying to get a base hit for example. I’m an African in England, but I daresay many more RBIs are produced from grounders and bunts than from HRs, no? However when a better does connect, on average there are probably many more RBIs gained from a successful swing for the fence than from the other less risky types of hits. From observation it seems many more hitters are caught out going for a HR. But that still doesn’t mean that the average HR will produces less runs by comparison.In conclusion I think that Dr Falkenstein is right; however his research doesn’t mean that the two are NOT mutually exclusive. “The more risk you take the more return you will get…….IF YOU ARE SUCCESSFUL!”

1. Dave Pinsen

Joe,The standard academic finance theory (of which the CAPM Fred referred to is a core part) essentially says the opposite: riskier assets should have higher returns. The logic behind that is that if they didn’t have higher returns, why would anyone buy them, if they could get similar or better returns in less risky assets? Hence, the idea of a risk premium to compensate investors for buying riskier assets.The problem is, as Falkenstein notes, decades of real-world data contradict this theory.________________________________

10. Mark Essel

Covariances and estimating them based on sampling large data sets is language I’m familiar with. The financial focus on beta is new to me though. I like the fact that it captures both correlation and magnitude. It’s interesting that in financial engineering the risk is mitigated by a large variance in your portfolio.A good buddy of mine at work is leaving to go into quant analysis at the NYC Carnegie Melon in a couple of weeks. I’ll keep in touch with him after he becomes a wizard to see if there may be easy to use products or tools his new industry might be interested in (beyond excel).

Hi Fred, Thanks for sharing some of your thoughts on investing and financial models.CAPM is a piece of crap, imho. It’s a really, really bad model to base most financial strategies on. CAPM is a triumph of the use of mathematics over thought.Why? Look at the assumptions:Assumptions of CAPMAll investors:Aim to maximize economic utility.Are rational and risk-averse.Are broadly diversified across a range of investments.Are price takers, i.e., they cannot influence prices.Can lend and borrow unlimited amounts under the risk free rate of interest.Trade without transaction or taxation costs.Deal with securities that are all highly divisible into small parcels.Assume all information is available at the same time to all investors.Perfect Competitive MarketsYou can use each assumption to spot areas to create returns (among other strategies).(Covariance is not a quantitative measurement of risk. It’s a formula based on flawed assumptions.)Hope these thoughts help y’all with your analyses… enjoy!P.S. Recommended reading: The Origin of Wealth, which has an excellent discussion of behavioral finance — which actually points out something very important in the financing of technology, interestingly!

1. fredwilson

i don’t really want to debate CAPM because i don’t feel qualified to do thatdo you think risk and return are correlated?

1. Bala

thanks, i think there are two parts to the answer.1) if we look at the parameter-space of all possible investments, there are definitely huge areas of investment-time space that are, for example, low return, high risk (v.c. in last 10 years, investing in films, throwing money from the top of a skyscraper, etc.), so it’s really hard to see correlation there if we are looking at the big picture. in other words, no.2) even if there is correlation, what does that really tell us… “The information given by a correlation coefficient is not enough to define the dependence structure between random variables. The correlation coefficient completely defines the dependence structure only in very particular cases, for example when the distribution is a multivariate normal distribution. “”These examples indicate that the correlation coefficient, as a summary statistic, cannot replace the individual examination of the data.” from wikipedia on correlationin investment, we don’t really care overall market generally, we’re more concerned about the existence of ways to make money. in reality we’re looking for pockets of the parameter-space that are actually low risk, high return (e.g. doing seed / early-stage investment in startups that are chosen through an excellent filter when not many others are focused on that market and using a combination of diversification and pyramid-ing up on successful investments where possible) due to being ignored by other participants in the market, and also systems for taking advantage of behavioral patterns in areas of the market that aren’t ignored, amongst other successful strategies. so really for many successful investors, it’s about finding investment plans that are low-risk that other people think are high-risk.additionally people often treat volatility as being equal to risk, which is not good. upward volatility should be welcomed and not penalized. (sortino ratio vs sharpe ratio.) also there are investment strategies that can produce steady returns, seemingly being of low risk, and then disappear to zero.when you write, “It doesn’t make sense for a young person to put all of their savings in a bank account unless they will need them soon. Because they can make a greater return by putting them into something where there is more risk.” it’s not really risk that one wants to look for, but higher upside. so we should focus on that to have a productive exploration.when you write, “Markets get out of whack sometimes. The tech stock market got out of whack in the late 90s. The subprime mortgage market got out of whack in the middle of the last decade. “, I am hearing someone who looks at the market through the lens of the equilibrium(/eff. market) model. But markets are a dynamical system. In a sense, one can consider the viewpoint that markets don’t get out of whack, but they appear to do so when we are looking at them through bad lenses / bad model.The model through which we look at markets can affect how we miss opportunities right in front of our eyes and how we manage our downside risks, so it is highly important that we use models that are not based on dramatically flawed assumptions that never really hold and were only put in place to make mathematical calculations easy.

12. PhilipSugar

The biggest problem with the chart is that return can be calculated risk cannot. They just fit the risk to match the return.You can’t be precise when one variable is precise and one is completely not precise.I was talking to two of my fraternity brothers in 2006 who were roomates of mine when I lived in NYC. Both managed huge mortgage backed portfolios for two top 20 banks. One had worked with Lou Ranieri in the late 80’s.I had just sold a house for double what I bought and when I saw the new buyers financing I had to get up and leave the table.I asked how could somebody possibly finance 110% of the value of an asset that had doubled to somebody who had no assets and had proven with a low 600 credit score they make bad financial decisions (frankly if you just looked at the paperwork they were signing they proved it)Both said their risk models along with diversification proved these piles of 100% dog crap were AAA credit risks. Go no further full stop. Finance people cannot evaluate risk.

1. John

I stopped reading your comment when you said “risk cannot be calculated”. Please stop spewing info if you don’t know what you’re talking about.

1. Bala

Hi John,Actually philsugar is right… Risk cannot be calculated. Read the work of Benoit Mandelbrot and Nassim Taleb. We think we can calculate risk, this notion is more dangerous than knowing that we cannot calculate risk. Imagine, if we were able to calculate risk all the major banks with sophisticated software and banking “experts” would have predicted the subprime crisis and stayed away from going neck deep into CDO and Sovereign debt of Greece etcRegards,Bala

13. ShanaC

Interesting- so this is where stat goes in….Hmm…how do you know if you have chosen an appropriate Beta if you are not using US treasuries- wouldn’t that beta represent the risk differential between your hedgible item versus some base.

14. sigmaalgebra

1. fredwilson

did i say that?i was just using CAPM to illustrate one model of the correlation between risk and return

1. sigmaalgebra

You are correct; you didn’t say that. Uh, I was trying to be brief and assumed we were talking also about venture investments.My main points remain, for all investments, venture or not:(1) Just given a set of candidate investments, without more assumptions, risk and return need not be correlated (yes, for investments, can accept assumptions sufficient so that the correlation coefficient always exists), i.e., can have correlation 0 or even have more risk brings less return. E.g., pick a VC or an IB and study his e-mail and see lots of high risk, low return!(2) The CAPM needs a lot of context, essentially some ideal version of the NYSE, and assumptions and does not hold for all sets of investments. The correlation and other effects in the CAPM are mostly artifacts of the market with many investors and the assumptions about it.(3) Risk and return are not immutable but, to be meaningful to an individual investor, depend on the information the investor has. That is, the investor should attempt to take conditional expectations conditioned on the information he has. Yes, the SEC and some academic economists floating around above the ozone want to assume that everyone has the same information about the NYSE stocks; lots of traders driving Ferraris want to laugh. In principle, and meaningfully in practice, an investor with enough information can get both low risk and high return.

15. usb flash drive

Covariances and assessment based on large data sample set is I’m familiar with the language. Beta on the financial focus is new to me though. I have the fact that it captures both the magnitude of correlation and the like. It is interesting that in financial engineering risk portfolio.A My good friend at work by a large variance in NYC at Carnegie Melon in quant analysis is going to be in a couple of weeks is reduced. I keep in touch with him after he becomes a wizard to see if there are simple products or equipment to your new industry can be used

16. CWall

Here’s a slightly different way of saying it that may help some of the novices who read the blog:As a rule, risk and reward are proportionate. You take more risk, you get a bigger return. Reduce risk, and you reduce your expected return.When risk and reward are proportionate, a market is said to be “efficient.”As a rule, the bigger the market, the more likely it is that the assets in that market are priced efficiently. That’s because bigger markets have more participants, and the more people looking at an investment, the more likely it is to be priced efficiently. Coca Cola is usually priced efficiently because it’s so widely studied.Now for the loophole:Although markets are often efficient, they’re not always efficient. From time to time, investments are priced stupidly, and the risk reward tradeoff is thrown out of whack.During the dot com boom, risk was high and the potential return was low. As a result, investors were taking a great deal of risk in exchange for a tiny potential return.On other occasions, the risk is low and the potential return is high. For example, when Warren Buffett invested in the Washington Post, any newspaper company on the planet would have purchased the company from its controlling shareholders for \$400 million. The stock was a bargain at \$200 million, and a screaming buy when the market cap dropped to \$100 million. That’s because the value of the post in a buyout was still \$400 million.In the example above, the decline from \$200 to \$100 million took risk off the table, while increasing the potential return. Ironically, those who rely on Beta would argue that the investment was actually riskier because it had fallen so much, and that’s where our notions of risk and reward fall short.Although risk and reward are often proportionate, they aren’t always proportionate.The trick to successful investing, VC or otherwise, is to find the rare opportunities where risk and reward are not proportionate.

17. Geoff

When you posted “The VC Math Problem” approximately a year ago, we exchanged e-mails discussing data derived from a valuation model that I developed (from the perspective from an outsider that only has publicly available information) and subsequently shared with you six months later. The valuation model employed a third party’s multi-factor regressional model with an adjusted R^2 (or correlation) of 0.83 at the 95% confidence level. While the model only explains 83% (rather than 100%) of the returns of VC investments for the period analyzed, it is a very good starting point for understanding the investment risks that LPs, GPs, and select employees assume in any period. It is also suggests a level of performance that the start-up should achieve – regardless of its unique risks of operations, etc. – in order for the expected returns to be realized. I am sure that better models are or will be available. For now, my valuation model seems to work quite well for a quick assessment of a start-up’s valuation range (rather than exact value, which lies in the eye of the beholder) in light of historical data, VC financing, stock market performance, as well as comparables. Financial models are like computer code/programs – they are only as good as the people that design, develop, test, and use them. People are ultimately the underlying risk of realizing upside returns or downside losses. The key is to try to “determine” and take calculated risks. That is what freedom is all about.

18. BenF

Not to take the focus off of risk, but its much more interesting to focus on the SCL, which correlates risk to alpha – the value created by the manager, or all VC managers.

19. Lloyd Fassett

I’m trying to figure out where CAPM comes into start up investing. Seems to me that high risk in start up word equates to doing something new with a lack of data that CAPM needs. It’s a time risk, not a financial risk like the chart in the post. High risk – high reward to me are things like CraigsList, Twitter, Deliscious and PlentyofFish because they were low cost but differentiated when launched and turned out to be high reward. Where do you find more of those?I’m looking forward to the diversification post because I would think that your constraining resource is your time, so how do you diversify that across ideas that don’t have traction vs. ones that do.