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In investment, there is often a discussion of risk. Investors are told to assess their own risk tolerance, funds and derivatives often advertise their own expected risk, and brokers ask for your risk tolerance both when opening accounts and for their screening/recommendation engines.

Confusingly, it seems that in these situations risk is measured using very ambiguous language: People speak of "high risk" or "low risk" or even "moderate risk". It seems that I am also expected to quantify my own risk in these terms, yet it's unclear what these terms even mean.

Presumably "high risk" means "you could lose all your money". But that isn't very helpful without a likelihood of the loss happening - for instance, the US Government could declare bankruptcy and I could lose all the money I put in treasury bills, but obviously few would call t-bills a high risk investment.

It appears that some sort of calculation is done (involving at least a histogram of loss magnitude vs. likelihood), and then the results are mapped onto these subjective categories like "high", "moderate" and "low". The calculation part seems straightforward - there is plentiful literature available on it so I am not asking about that. What I'd like to know is, how does the mapping to these subjective terms happen?

Specifically, what does my broker mean when they say an asset or investment strategy is high risk? What does my ETF mean when they claim in the prospectus to be low risk? How am I supposed to answer a question like "rate your risk tolerance from low to high"?

Addendum on 3/29/2016: Perhaps my confusion stems from the fact that my willingness to take on risk is naturally dependent on expected gain. I know this relationship can be formalized, eg. with the Sharpe ratio. However, this does make the question of risk tolerance more confusing - I will refuse (as any rational person) even very tiny risk for poor Sharpe, and I would strongly consider even very large risk if Sharpe is good. Of course, past Sharpe does not guarantee future Sharpe... So what is the assumed Sharpe ratio for these sorts of questions about risk tolerance?

  • If I understand you correctly, you are asking for a 'formula' of sorts to map these terms to a quantity. I know of no such mapping. It is like when you go to the doctor and he asks you to rate your pain from 1 to 5. The answer will always be subjective. – Jack Swayze Sr Mar 23 '16 at 4:47
  • Yet, for instance, when opening a margin account you are required (for legal reasons) to confirm that you understand it is "high risk". How do you answer this? – Superbest Mar 23 '16 at 4:50
  • If you can't answer that, you shouldn't be claiming you understand it... or putting any nontrivial amount of money into it. That's precisely why they are asking. – keshlam Mar 23 '16 at 5:35
  • It is possible to get a rough handle on what kinds of investment you would be comfortable with by looking at how patient you would be in waiting out downturns, accepting losses from time to time, etc. and what your goals and timeframe are for the money. This is one of the things a real financial advisor can help you determine. Generally, high risk should be a small part of your portfolio -- nothing you couldn't afford to lose -- if you play with it at all. – keshlam Mar 23 '16 at 5:43
  • @superbest How do I answer? As with all subjective criteria, based on my 'gut'. – Jack Swayze Sr Mar 23 '16 at 7:31
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Defining risk tolerance is often aided with a series of questions. Such as - You are 30 and have saved 3 years salary in your 401(k). The market drops 33% and since you are 100% S&P, you are down the same. How do you respond? (a) move to cash - I don't want to lose more money. (b) ride it out. Keep my deposits to the maximum each year. Sleep like a baby.

A pro will have a series of this type of question. In the end, the question resolves to "what keeps you up at night?" I recall a conversation with a coworker who was so risk averse, that CDs were the only right investment for her. I had to explain in painstaking detail, that our company short term bond fund (sub 1 year government paper) was a safe place to invest while getting our deposits matched dollar for dollar. In our conversations, I realized that long term expectations (of 8% or more) came with too high a risk for her, at any level of her allocation. Zero it was.

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It really centers on the probability of your position falling to $0 and your level of comfort if that were to happen. There are a plethora of situations that could cause an option contract to become worthless. The application of leverage to a position also increases the risk.

Zero risk would be an FDIC insured savings account, high risk would be buying options on margin, and there's a very wide grey area in between. I agree that the whole process of assigning a risk level is dubious at best. As you say, it seems using past data could help assign a risk level, look to beta values if you believe in that. The problem here is the main disclaimer in use is that past performance cannot be relied upon for future gains.

As an aside, if the US government files bankruptcy you'll have a whole host of more immediate problems than the value of your t-bills. At that point dollars would have been a risky investment.

  • The United States Federal government cannot go bankrupt according to the 14th amendment… Amendment XIV " Section 4a. " The validity of the public debt of the United States, authorized by law, including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion, shall not be questioned." – Jack Swayze Sr Mar 23 '16 at 7:40
  • @JackSwayzeSr, He raises the US government filing bankruptcy, I was just addressing it. What I mean to say is if the US government ever got to that level of turmoil, financially or otherwise, there would be much more pressing issues than redeeming some t-bills. – quid Mar 23 '16 at 16:51
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    Sorry, I was addressing superbest, not you. To superbest the debt of the US Federal government is 'unquestionable' by the 14th amendment. Many have interpreted this as a fundamental obligation by the US to pay its debts. It is part of the reason that Yellen questioned if negative interest rates, paid by the Fed on overnight funds, were even legal. – Jack Swayze Sr Mar 23 '16 at 17:24
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In addition to what quid said, I think your risk tolerance should depend on how likely you are to need the funds in the near future. Say that you have $100k saved up and you want to decide how to invest it. Then you should ask yourself:

  • How much do you want to set aside for a rainy day? Since you don't know when the rainy day will be, you should probably asign a very low risk to this portion
  • Do you have any outgoings that you know will come soon? Then again you should assign very low risk (ie cash and government bonds with not maturing too far in the future, let's say less than 2 years)
  • Any excess on top of that you can split between medium and high risk (depending on whether you think you'll need some of it in medium or long term)

The idea here is that if you invest say in stocks (high risk) then the value of your position could drop significantly and you'd potentially have to wait for a long time before it recovers. If you are forced to sell you could make a substantial loss. If you don't urgently need this cash, however, then you can feel relaxed and just wait for the market to reverse again. This is viewing risk through the lens of how likely it is that you'll have to wait a long time to get a substantial amount of your money back, which itself is a function of how likely it is for a substantial downturn to occur in a certain market.

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Specifically, what does my broker mean when they say an asset or investment strategy is high risk?

In this context, it is a statement based on past events and probability. It is based on how confident s/he is that the investment will perform to certain benchmarks. This is a math question, primarily (with some opinion mixed in, granted). This is where the Sharpe ratio and others fit well.

How am I supposed to answer a question like "rate your risk tolerance from low to high"?

This is the hard question, as you have seen. In this context, risk tolerance is derived from your current position and future plans (goals). This is a planning, goal setting, and strategy question, primarily (with some math mixed in, granted). How vulnerable is your current position and future plans to an under-performing investment? If you answer "very", then you choose investments that have a lower probability of under-performing.

The Sharpe ratio has little to do with answering this question. It is a tool to find investments that better match your answer to this question.

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