Risk Adjusted Return?

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Leeraar
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Risk Adjusted Return?

Post by Leeraar » Sun Jul 06, 2014 2:28 pm

I am looking at two investment strategies for which I have total return prices monthly for 25+ years. If I look at each yearly interval (starting each month) I have:

Investment A: Average return 10.99%, Standard deviation of return 17.24%.

Investment B: Average return 5.95%, Standard deviation of return 9.94%.

As a first approximation of risk,

Investment A: 10.99/17.24 = 0.64
Investment B: 5.95 / 9.94 = 0.60

So, investment A is slightly less risky. Am I on the right track?

It seems any positive risk-free return will simply make Investment B look worse in calculating something like a Sharpe Ratio. Note that I am using standard deviation of return, not of price.

Any advice or criticism will be gratefully received.

L.
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Re: Risk Adjusted Return?

Post by nisiprius » Sun Jul 06, 2014 2:46 pm

One usual measure of risk-adjusted return is the Sharpe ratio. If you assume that the "riskless asset"--cash, money market accounts, what have you--returns 0%, which is reasonable enough today, then the Sharpe ratio is just what you've calculated and you are on the right track.

In "normal" times, the riskless asset might have a meaningful return. That needs to be taken into account. It's always true that the return of a mix is the mix of the returns. That is, if asset A has a return of 5% and asset B has a return of 15% then the return of a 50/50 mix of the two assets will be the midpoint of the two returns, or 10%. In general, this is NOT true for standard deviations. The curve showing the mix is one of those hyperbolas, the risk of the mix is less than you'd get by calculating the percentage mix of the standard deviations, the amount of the bulge depends on the correlation,

For the special case of a riskless asset, though, (standard deviation is zero), then the correlation is always zero, too. The plot of the mix of a riskless asset and a risky asset on a return-versus-S.D. chart is a straight line, and the standard deviation of a mix is just the algebraic mix of the standard deviations.

Now, consider asset A with return 10 and standard deviation 10, and asset B with return 20 and standard deviation 20. Are they equally good investments? If the return on the riskless investment is zero, yes, they are.

However, if the riskless asset has a return of, let's say 10, then B is a better investment. Why? Because when you mix in the riskless asset to mellow its standard deviation, if you use 1/2 B and 1/2 riskless, you get 1/2 the standard deviation, but you get more than 1/2 the return because the riskless asset is contributing its own return. Specifically, a 50/50 mix of the riskless asset and asset B will have a standard deviation that is the midpoint or average of 0 and 20 = 10. But, it will have a return that is the midpoint or average, not of 0 and 20, but of 10 and 20, or 15.

Asset A: Standard deviation 10, return 10.
50% asset B + 50% riskless: standard deviation 10, return 15.

I'm not too clear myself on how you go about calculating a Sharpe ratio in practice, but the general idea is that instead of dividing the return by the standard deviation, which is what you did, you use, not the return, but the excess return--the extra return that the investment has above and beyond the return of the riskless asset.
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Re: Risk Adjusted Return?

Post by richard » Sun Jul 06, 2014 2:56 pm

What are you trying to do?

Standard deviation is not a very good measure of risk. It's simple and easy to calculate, but doesn't match well with more intuitive notions of risk, such as not having enough money when you need it or doing badly in bad times. Unfortunately, there isn't a very good quantification of risk (unless all you care about are mean return and variance).

You're looking at past performance. Are you doing this because you believe it will provide a good guide to the future?

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Re: Risk Adjusted Return?

Post by Taylor Larimore » Sun Jul 06, 2014 3:03 pm

Leeraar wrote:So, investment A is slightly less risky. Am I on the right track?
Leeraar:

Investment "A" WAS "slightly less risky." Unfortunately for investors, It is impossible to forecast future stock performance (risk and return) based on past performance.

This post by Ozark is insightful:
................................................PREDICTING THE PAST............................................

If you feel you can improve your portfolio's asset allocation by running the portfolio through various computer programs, measuring and grading various risk/reward relationships, feel free. It's okay with me. Honest. For myself, I'm not interested.

I'm also not interested in running reams of data through a computer program in order to discover how much I can withdraw yearly from my portfolio and never go broke.

Without having studied it, I'm willing to assume the Risk Grades deal is similar to the well known Efficient Frontier concept: Invest in a mix of assets that will give the best return for the least risk.

Wonderful. The problem in execution is this; both these approaches would seem to be limited to looking at PAST risk/return relationships, in order to predict FUTURE such relationships.

This approach hasn't worked very well and it never will.

There's lots of stuff we can learn by studying the past. One thing we can't learn, though, is how much the future will resemble the past.

There really is an Efficient Frontier. There really is a withdrawal rate that will allow my wife and I to spend all our money during our life times, but never go broke.

But these things are unknown and unknowable, going forward. Such things are only knowable looking backward.

Given that such things are only knowable looking backward, academics with more letters after their names than I have money in the bank, have spent unconscionable amounts of time goobering through the past. They thus invented Modern Portfolio Theory---Beta, Alpha, R-Squared, and the crowning achievement, Sharpe Ratio. These accomplishments were celebrated and awards were given. Yes.

And then...a funny thing happened on the way to the bank. These numbers turned out to have little or no predictive value, regarding returns. And since they couldn't predict returns, they also failed to predict risk/return ratios.

Joining in the fun, M* invented their first Star Rating system, a system that graded...yep...risk- adjusted, past performance.

I wish I had 10 bucks for every post I've read where the poster said, essentially, "I have a balanced portfolio, made up entirely of 4 and 5 star funds." Too late, these jokers discovered what M* eventually discovered; past risk-adjusted performance doesn't predict future risk-adjusted performance.

I don't want to discover the Sharpe Ratio of my portfolio. I don't want to discover its Beta. I don't want to discover its Risk Grade. I have absolutely no confidence that adjusting the portfolio so that these numbers become more favorable will improve future risk/reward.

If others do want to do that, that's okay with me. I seriously doubt, though, that many successful mutual fund managers select securities in that manner. If any do, or if any money managers set their asset allocations in that manner, I'd be interested in their long-term results---results over periods of, say, 10 years, or more.

In short, computers are wonderous tools, but that's all they are. Every computer on Earth, all linked up and working 24/7, from now on, won't tell me my survivable withdrawal rate. Neither will they tell me what asset allocation would give me the best risk/reward ratio.

In my opinion, these things can't be calculated. We have to forge ahead without knowing these things. Deal with it.
Best wishes.
Taylor
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Re: Risk Adjusted Return?

Post by Kevin M » Sun Jul 06, 2014 3:09 pm

Leeraar wrote: Investment A: 10.99/17.24 = 0.64
Investment B: 5.95 / 9.94 = 0.60

So, investment A is slightly less risky. Am I on the right track?
No, investment A is more risky. A higher risk-adjusted return does not mean the investment is less risky. It might be called more efficient.

All of this assumes that standard deviation of past monthly returns is a valid measure of risk, which of course may not be the case.

I don't think standard deviation necessarily is a poor conceptual measure of risk, but the problem is that we don't know the standard deviation of expected returns for our future holding period (we don't even know the expected return).

Kevin
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Re: Risk Adjusted Return?

Post by acegolfer » Sun Jul 06, 2014 3:28 pm

richard wrote:What are you trying to do?

Standard deviation is not a very good measure of risk. It's simple and easy to calculate, but doesn't match well with more intuitive notions of risk, such as not having enough money when you need it or doing badly in bad times. Unfortunately, there isn't a very good quantification of risk (unless all you care about are mean return and variance).

You're looking at past performance. Are you doing this because you believe it will provide a good guide to the future?
Unless we (or you) can come up with a better measure of risk than stdev, unfortunately, we don't have much choice.

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Re: Risk Adjusted Return?

Post by richard » Sun Jul 06, 2014 3:35 pm

acegolfer wrote:Unless we (or you) can come up with a better measure of risk than stdev, unfortunately, we don't have much choice.
There are at least two choices

1) Realize that the enterprise is not helpful for forward looking purposes, such as choosing an asset allocation or choosing investments to use for your allocation. Read Taylor's excellent post. Consider the limited data available and the inapplicability to finance of standard statistics which presume an unchanging underlying distribution.

2) If you nonetheless feel you must quantify, use a better measure of risk. There are numerous multi-factor models and models which tie returns to macro-economic factors. Some of the multi-factor models do a better job of explaining past returns than stdev (and it's friend, CAPM). The Fama-French three factor model is rather popular in these parts.

The threshold question continues to be what the OP intends to accomplish.
Last edited by richard on Sun Jul 06, 2014 3:38 pm, edited 1 time in total.

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Re: Risk Adjusted Return?

Post by packer16 » Sun Jul 06, 2014 3:38 pm

I think part of the problem is risk tolerance is different for different folks. So something with alot of volatility may be too risky for one person irregardless of expected return but not to another if the expected return is high enough. Therefore, this is a personal question. What types of assets underlie the historical returns? If we know this, then we may be able to ask the second and also important question of is there are reasonable chance of achieving the historical performance and receiving a reward for taking on the risk?

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Re: Risk Adjusted Return?

Post by acegolfer » Sun Jul 06, 2014 3:54 pm

richard wrote: There are at least two choices

1) Realize that the enterprise is not helpful for forward looking purposes, such as choosing an asset allocation or choosing investments to use for your allocation. Read Taylor's excellent post. Consider the limited data available and the inapplicability to finance of standard statistics which presume an unchanging underlying distribution.

2) If you nonetheless feel you must quantify, use a better measure of risk. There are numerous multi-factor models and models which tie returns to macro-economic factors. Some of the multi-factor models do a better job of explaining past returns than stdev (and it's friend, CAPM). The Fama-French three factor model is rather popular in these parts.

The threshold question continues to be what the OP intends to accomplish.
TY for quick response. First of all, I agree that stdev has flaws. We just have to know its limitation when using it to measure risk.

3 comments to your post.
1. I don't know how to objectively compare the performance without quantifying. Can you answer OP's question without quantifying?
2. There standard methods to use CAPM to evaluating performance. See Treynor ratio, which is expected excess return / beta or Jensen's alpha.
http://en.wikipedia.org/wiki/Treynor_ratio

The wiki also states its limitations.
Like the Sharpe ratio, the Treynor ratio (T) does not quantify the value added, if any, of active portfolio management. It is a ranking criterion only. A ranking of portfolios based on the Treynor Ratio is only useful if the portfolios under consideration are sub-portfolios of a broader, fully diversified portfolio. If this is not the case, portfolios with identical systematic risk, but different total risk, will be rated the same. But the portfolio with a higher total risk is less diversified and therefore has a higher unsystematic risk which is not priced in the market.
An alternative method of ranking portfolio management is Jensen's alpha, which quantifies the added return as the excess return above the security market line in the capital asset pricing model. As these two methods both determine rankings based on systematic risk alone, they will rank portfolios identically.
In addition, I think we can't use Treynor ratio for non-stock portfolios.

3. There are controversial views on whether the SMB and HML are risk factors because explaining cross section returns using these factors doesn't necessarily mean they are risk factors. It seems you consider these 2 as risk factors.

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Re: Risk Adjusted Return?

Post by acegolfer » Sun Jul 06, 2014 4:12 pm

@OP,

How did you calculate the average returns of your 2 investment strategies?

There are at least 3 methods to calculate the average return.

1. AAR
2. GAR
3. DWR

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Re: Risk Adjusted Return?

Post by Leeraar » Sun Jul 06, 2014 9:29 pm

nisiprius wrote:One usual measure of risk-adjusted return is the Sharpe ratio. If you assume that the "riskless asset"--cash, money market accounts, what have you--returns 0%, which is reasonable enough today, then the Sharpe ratio is just what you've calculated and you are on the right track.

In "normal" times, the riskless asset might have a meaningful return. That needs to be taken into account. It's always true that the return of a mix is the mix of the returns. That is, if asset A has a return of 5% and asset B has a return of 15% then the return of a 50/50 mix of the two assets will be the midpoint of the two returns, or 10%. In general, this is NOT true for standard deviations. The curve showing the mix is one of those hyperbolas, the risk of the mix is less than you'd get by calculating the percentage mix of the standard deviations, the amount of the bulge depends on the correlation,

For the special case of a riskless asset, though, (standard deviation is zero), then the correlation is always zero, too. The plot of the mix of a riskless asset and a risky asset on a return-versus-S.D. chart is a straight line, and the standard deviation of a mix is just the algebraic mix of the standard deviations.

Now, consider asset A with return 10 and standard deviation 10, and asset B with return 20 and standard deviation 20. Are they equally good investments? If the return on the riskless investment is zero, yes, they are.

However, if the riskless asset has a return of, let's say 10, then B is a better investment. Why? Because when you mix in the riskless asset to mellow its standard deviation, if you use 1/2 B and 1/2 riskless, you get 1/2 the standard deviation, but you get more than 1/2 the return because the riskless asset is contributing its own return. Specifically, a 50/50 mix of the riskless asset and asset B will have a standard deviation that is the midpoint or average of 0 and 20 = 10. But, it will have a return that is the midpoint or average, not of 0 and 20, but of 10 and 20, or 15.

Asset A: Standard deviation 10, return 10.
50% asset B + 50% riskless: standard deviation 10, return 15.

I'm not too clear myself on how you go about calculating a Sharpe ratio in practice, but the general idea is that instead of dividing the return by the standard deviation, which is what you did, you use, not the return, but the excess return--the extra return that the investment has above and beyond the return of the riskless asset.
nisiprius,

Thank you. My understanding agrees with what you say.

M=(R-A)/S

M = measure of risk
R = rate of return
A = Riskless rate of return
S = Standard deviation of return

and I have A = zero. In my case, any positive value of A will make Investment A look better. (For M, higher is better.)

I also agree with what you say about the standard deviation of a mix of investments. That issue does not apply here.

L.
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Re: Risk Adjusted Return?

Post by Leeraar » Sun Jul 06, 2014 9:32 pm

Taylor Larimore wrote:
Leeraar wrote:So, investment A is slightly less risky. Am I on the right track?
Leeraar:

Investment "A" WAS "slightly less risky." Unfortunately for investors, It is impossible to forecast future stock performance (risk and return) based on past performance.

Taylor
Taylor,

Thank you for the reminder. I am fully aware these things are only visible in a rear view mirror.

L.
Last edited by Leeraar on Sun Jul 06, 2014 11:01 pm, edited 1 time in total.
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Re: Risk Adjusted Return?

Post by Leeraar » Sun Jul 06, 2014 9:48 pm

richard wrote:What are you trying to do?

Standard deviation is not a very good measure of risk. It's simple and easy to calculate, but doesn't match well with more intuitive notions of risk, such as not having enough money when you need it or doing badly in bad times. Unfortunately, there isn't a very good quantification of risk (unless all you care about are mean return and variance).

You're looking at past performance. Are you doing this because you believe it will provide a good guide to the future?
Richard,

I am trying to assess the relative risk of two investment strategies. There is nothing in either strategy that is "tuned" by historical data. All I want to say is, "This is what has happened in the past".

What I have is a list of one-year returns for each strategy per month over 25 years: About 300 values. How can I compare the relative risk?

L.
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Re: Risk Adjusted Return?

Post by Leeraar » Sun Jul 06, 2014 10:10 pm

acegolfer wrote:@OP,

How did you calculate the average returns of your 2 investment strategies?

There are at least 3 methods to calculate the average return.

1. AAR
2. GAR
3. DWR
Ace,

I have a spreadsheet of historical data. I am interested in, what happens if you apply each strategy for a year? So, starting on any given (monthly) date I can calculate the return of Investment A or Investment B over the following year. For each of 12 months over 25 years I now have about 300 values. What I am quoting are the Excel averages AVERAGE() and standard deviations STDEV.P() of these 300 yearly return numbers for each of Investment A and Investment B. Which is riskier?

My sense is, the adjusted risk is about the same, borne out by the calculation in the OP. Would you agree?

To be quite honest, I was surprised to Google "risk-adjusted return" and to find what seems to me to be a bunch of hand waving.

L.
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Re: Risk Adjusted Return?

Post by magician » Sun Jul 06, 2014 11:51 pm

richard wrote:2) If you nonetheless feel you must quantify, use a better measure of risk. There are numerous multi-factor models and models which tie returns to macro-economic factors. Some of the multi-factor models do a better job of explaining past returns than stdev (and it's friend, CAPM). The Fama-French three factor model is rather popular in these parts.
And how, exactly, do you use the betas in Fama-French to quantify risk? If one security has a market beta of 0.8, a size beta of 1.2 and a value beta of 1.3, while another has, respectively, 1.2, 0.5, and 1.5, which one is riskier? Why?

(As a side note, Fama-French is no less dependent on a security's standard deviation of returns than is CAPM; if σ is CAPM's friend, it's equally Fama-French's friend.)
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Re: Risk Adjusted Return?

Post by Leeraar » Mon Jul 07, 2014 12:07 am

For example,

http://www.morningstar.com/InvGlossary/ ... eturn.aspx
Risk-Adjusted Return

A measure of how much money your fund made relative to the amount of risk it took on over a specific time period.

If two funds had a 10% return, the less risky fund would have a better risk-adjusted return. The Morningstar Star Rating is one measure of risk-adjusted return.
And, don't we know the Morningstar star rating is more or less useless?

L.
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Re: Risk Adjusted Return?

Post by moshe » Mon Jul 07, 2014 12:24 am

Leeraar,

Can you tell us how you annualized the SD and the return? Normally you would have to take the SD of the series and then multiply it by the SQRT(12) to annualized the SD value assuming that you based it on monthly data points. The excess return should be annualized by applying the following formula after you figure the average monthly excess return : ((1+ExRet)^12)-1. Is this what you did?

Also, why not use BIL (SPDR Barclays 1-3 Month T-Bill) to represent the riskless rate and minus it from the monthly return to produce the excess return before you figure your Sharpe, beta and then Treynor? Ignoring the risk free rate over the past 25 years would turn your data into useless numbers I fear.

Not for the feint of heart but you could also use Excel's solver and matrix math(mmult) utilizing a Var_Covar table to be able to figure out the lowest portfolio variance based on a weighting of two, three, thirty or more assets.

As has been said above all these are based on historical numbers so....well...you know what they really represent....the past.

~Moshe
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Re: Risk Adjusted Return?

Post by Leeraar » Mon Jul 07, 2014 5:16 am

moshe wrote:Leeraar,

Can you tell us how you annualized the SD and the return? Normally you would have to take the SD of the series and then multiply it by the SQRT(12) to annualized the SD value assuming that you based it on monthly data points. The excess return should be annualized by applying the following formula after you figure the average monthly excess return : ((1+ExRet)^12)-1. Is this what you did?

Also, why not use BIL (SPDR Barclays 1-3 Month T-Bill) to represent the riskless rate and minus it from the monthly return to produce the excess return before you figure your Sharpe, beta and then Treynor? Ignoring the risk free rate over the past 25 years would turn your data into useless numbers I fear.

Not for the feint of heart but you could also use Excel's solver and matrix math(mmult) utilizing a Var_Covar table to be able to figure out the lowest portfolio variance based on a weighting of two, three, thirty or more assets.

As has been said above all these are based on historical numbers so....well...you know what they really represent....the past.

~Moshe
Moshe,

I did not annualize anything. I just calculated return as

r = (E - I)/I

r = return
E = end value
I = amount invested

for each one-year period. So, I have about 300 one-year return values. The standard deviation is simply the excel function STDEV.P of these 300 numbers.

L.
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Re: Risk Adjusted Return?

Post by acegolfer » Mon Jul 07, 2014 5:39 am

Leeraar wrote:
Ace,

I have a spreadsheet of historical data. I am interested in, what happens if you apply each strategy for a year? So, starting on any given (monthly) date I can calculate the return of Investment A or Investment B over the following year. For each of 12 months over 25 years I now have about 300 values. What I am quoting are the Excel averages AVERAGE() and standard deviations STDEV.P() of these 300 yearly return numbers for each of Investment A and Investment B. Which is riskier?

My sense is, the adjusted risk is about the same, borne out by the calculation in the OP. Would you agree?

To be quite honest, I was surprised to Google "risk-adjusted return" and to find what seems to me to be a bunch of hand waving.

L.
There was a similar thread about how to calculate return and stdev. Follow his method at the end. (The difference is he calculated nominal return. So you must subtract monthly riskless return for every month, which is not 0% in the last 25 years.)
http://www.bogleheads.org/forum/viewtop ... ilit=stdev

I think you are confused between yearly return and monthly return. If you have 25 yrs of data, then you can't have 300 yearly returns. It's either 25 yearly returns or 300 monthly returns.

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Re: Risk Adjusted Return?

Post by moshe » Mon Jul 07, 2014 6:54 am

Leeraar wrote: Moshe,

I did not annualize anything. I just calculated return as

r = (E - I)/I

r = return
E = end value
I = amount invested

for each one-year period. So, I have about 300 one-year return values. The standard deviation is simply the excel function STDEV.P of these 300 numbers.

L.
Hi L.,

Here is the way i would do it:

1) take the monthly adjusted close prices (removes the effects of dividends and stock splits)
2) to figure return:

(CurM/PrevM)-1

3) result from #2 minus BIL from CurM will produce a RiskFree (RF) return (RFRet).

Take the average of the RFRet's to find an average RFRet.
Take the STDEV.S (you are sampling as you do not have every daily return for the period) of the series.

Annualize using the formula's from my previous post. Now you can figure Sharpe, Beta, Treynor and alpha.

~Moshe

P.S. To figure the Beta and then alpha you will also need the same average RFRet for ^GSPC (the S&P500) or the VTI (Total market) or some other benchmark to act at the market. The SD might be interesting as well for comparison sake.
Last edited by moshe on Mon Jul 07, 2014 6:59 am, edited 1 time in total.
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Re: Risk Adjusted Return?

Post by richard » Mon Jul 07, 2014 6:59 am

Leeraar wrote:
richard wrote:What are you trying to do?

Standard deviation is not a very good measure of risk. It's simple and easy to calculate, but doesn't match well with more intuitive notions of risk, such as not having enough money when you need it or doing badly in bad times. Unfortunately, there isn't a very good quantification of risk (unless all you care about are mean return and variance).

You're looking at past performance. Are you doing this because you believe it will provide a good guide to the future?
Richard,

I am trying to assess the relative risk of two investment strategies. There is nothing in either strategy that is "tuned" by historical data. All I want to say is, "This is what has happened in the past".

What I have is a list of one-year returns for each strategy per month over 25 years: About 300 values. How can I compare the relative risk?

L.
This is a purely academic exercise rather than a way to decide on an investment strategy for the future?

Depends on what you mean by risk. Not everyone believes in the same definition.

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Re: Risk Adjusted Return?

Post by richard » Mon Jul 07, 2014 7:07 am

magician wrote:
richard wrote:2) If you nonetheless feel you must quantify, use a better measure of risk. There are numerous multi-factor models and models which tie returns to macro-economic factors. Some of the multi-factor models do a better job of explaining past returns than stdev (and it's friend, CAPM). The Fama-French three factor model is rather popular in these parts.
And how, exactly, do you use the betas in Fama-French to quantify risk? If one security has a market beta of 0.8, a size beta of 1.2 and a value beta of 1.3, while another has, respectively, 1.2, 0.5, and 1.5, which one is riskier? Why?

(As a side note, Fama-French is no less dependent on a security's standard deviation of returns than is CAPM; if σ is CAPM's friend, it's equally Fama-French's friend.)
Why do you think risk can be reduced to a single number? A major point of factor models with more than one factor is that there is more than one dimension to risk. An investment can have more of one type of risk and less of another. A related problem with many of these models is that their factors proxy for an unidentified economic risk rather than being actual risks.

Do you believe standard deviation captures everything we think of as risk for securities?

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Re: Risk Adjusted Return?

Post by moshe » Mon Jul 07, 2014 7:14 am

richard wrote: This is a purely academic exercise rather than a way to decide on an investment strategy for the future?

Depends on what you mean by risk. Not everyone believes in the same definition.
Richard,

In my opinion for asset allocation purposes there is value in doing this type of analysis as long as you are looking at broad market segments(REIT, X-US, etc.) and not individual securities.

~Moshe
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Re: Risk Adjusted Return?

Post by nisiprius » Mon Jul 07, 2014 7:27 am

One problem with all measures of risk is "how much data do you need to have to get a valid measurement?" Have you noticed that almost nobody ever talks about this? In ordinary writing, writers simply try to impress you by mentioning how much data has been used, without ever saying how much data would be needed.

I've (finally) been reading Kahneman's "Thinking, Fast and Slow" and was amazed by what he says about what he calls the "law of small numbers." He found that psychologists habitually and consistently plan experiments in which they decide how many trials they need by using their statistical intuition, instead of actually calculating the number--and their intuition is lousy and they very consistently use far too small a number of trials.

Standard deviation itself is bad enough. It takes far more samples to estimate standard deviation accurately than it does to estimate a mean. I've already discovered, if that's the name for it, that "the historic return of the stock market," just the plain old return over the period everyone mentions--1926 to present--can come out as anything from 9% to 11% if you just move the endpoints a few years. The fluctuations are so big that they can influence a sample eight or nine decades long. I ought to try the same exercise with standard deviation, I'll put it on my mental "to-do" list.

Now it's easy enough to say "my personal measure of risk is 'extreme negative events.'" And maybe that can be defended as much more relevant than standard deviation. The problem is that it is far harder to estimate the probability of rare and extreme events than it is to estimate a standard deviation (which is a sort of broad-brush measure of fluctuations of all sizes).
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Re: Risk Adjusted Return?

Post by acegolfer » Mon Jul 07, 2014 8:46 am

IMO, this thread is going out of control and there will be no consensus on how to define risk.

Can we go back to the OP's question and answer it? If you can come up with a method to calculate the risk adjusted return, please suggest it. Otherwise, it is not going to help OP.

(If you really want to debate on the definition of risk, why not create another thread so that it draws more opinion?)

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Re: Risk Adjusted Return?

Post by magician » Mon Jul 07, 2014 9:12 am

richard wrote:
magician wrote:
richard wrote:2) If you nonetheless feel you must quantify, use a better measure of risk. There are numerous multi-factor models and models which tie returns to macro-economic factors. Some of the multi-factor models do a better job of explaining past returns than stdev (and it's friend, CAPM). The Fama-French three factor model is rather popular in these parts.
And how, exactly, do you use the betas in Fama-French to quantify risk? If one security has a market beta of 0.8, a size beta of 1.2 and a value beta of 1.3, while another has, respectively, 1.2, 0.5, and 1.5, which one is riskier? Why?

(As a side note, Fama-French is no less dependent on a security's standard deviation of returns than is CAPM; if σ is CAPM's friend, it's equally Fama-French's friend.)
Why do you think risk can be reduced to a single number?
I don't.
richard wrote:A major point of factor models with more than one factor is that there is more than one dimension to risk. An investment can have more of one type of risk and less of another. A related problem with many of these models is that their factors proxy for an unidentified economic risk rather than being actual risks.
There is more than one type of risk; whether different types should be classified as "dimensions" is another matter entirely.

You suggested that the Fama-French model is a better measure of risk. I was simply asking how you would use it to determine which of two securities is riskier (which is, after all, what the original post was trying to determine). It appears that your position now is that it cannot. Should that be the case, we agree.
richard wrote:Do you believe standard deviation captures everything we think of as risk for securities?
Not remotely.

Do you believe that multi-factor models capture everything we think of as risk for securities?
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Re: Risk Adjusted Return?

Post by Leeraar » Mon Jul 07, 2014 10:13 am

OP here. Thank you all, I think I have what i was looking for.

For any riskless return that is positive, Investment A has a larger Sharpe Ratio than Investment B.

I must admit I was surprised to find how much slop there is in the idea of "Risk Adjusted Return", at least for equities. It makes me wonder how the slice and dice / tilting crowd can assess if what they're doing is doing them any good.

L.
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Re: Risk Adjusted Return?

Post by moshe » Mon Jul 07, 2014 2:31 pm

Leeraar wrote:OP here.

I must admit I was surprised to find how much slop there is in the idea of "Risk Adjusted Return", at least for equities. It makes me wonder how the slice and dice / tilting crowd can assess if what they're doing is doing them any good.

L.
Here is what i would do:

RET = (P2-P1+div)/P1

P1 = Initial Outgoing

P2 = End of Period Incoming

div = collected dividends.

RET = % return

Do this calculation for GSPC or VTI and then for your "tilted" portfolio and compare.

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Re: Risk Adjusted Return?

Post by Kevin M » Mon Jul 07, 2014 7:00 pm

Leeraar wrote:It makes me wonder how the slice and dice / tilting crowd can assess if what they're doing is doing them any good.
Here's one way we can tell (blue = VG small-cap value, orange = VG 500 index):

Image

We don't necessarily think we're getting a higher risk-adjusted return. Some of us think that we are (or at least may be) getting exposure to an additional risk factor that has a higher expected return (and higher risk) than the market risk factor.

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Re: Risk Adjusted Return?

Post by Kevin M » Mon Jul 07, 2014 7:15 pm

To be fair, a tilt to value using VG Value Index hasn't done a tilter much good over the time period shown above, and VG small-cap growth has done about as well as small-cap value, so it's really the tilt to small-cap that has paid off over this time period--at least with Vanguard funds. However, as Bill Bernstein has pointed out, DFA large-cap value has done much better over the same time period, so apparently the Vanguard large value fund didn't do a good job of capturing the value premium over this period. Still, a tilt to small-cap has done much better than a tilt to value over this period.

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Re: Risk Adjusted Return?

Post by Leeraar » Mon Jul 07, 2014 7:24 pm

Kevin M wrote:
Leeraar wrote:It makes me wonder how the slice and dice / tilting crowd can assess if what they're doing is doing them any good.
Here's one way we can tell (blue = VG small-cap value, orange = VG 500 index):

Image

We don't necessarily think we're getting a higher risk-adjusted return. Some of us think that we are (or at least may be) getting exposure to an additional risk factor that has a higher expected return (and higher risk) than the market risk factor.

Kevin
Kevin,

Thank you, very interesting.

In your example, I am looking for: We have VG 500 and its return and its risk measure (standard deviation, beta). And, we have Small-Cap Value and its beta. With those three bits of information, can I calculate an expected (risk-adjusted) return for SCV to compare against the actual return? Trying to answer the question, is the extra return worth the extra risk?

L.
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Re: Risk Adjusted Return?

Post by Leeraar » Mon Jul 07, 2014 7:38 pm

moshe wrote:
Leeraar wrote:OP here.

I must admit I was surprised to find how much slop there is in the idea of "Risk Adjusted Return", at least for equities. It makes me wonder how the slice and dice / tilting crowd can assess if what they're doing is doing them any good.

L.
Here is what i would do:

RET = (P2-P1+div)/P1

P1 = Initial Outgoing

P2 = End of Period Incoming

div = collected dividends.

RET = % return

Do this calculation for GSPC or VTI and then for your "tilted" portfolio and compare.

~Moshe
Moshe,

I have that part, thank you. It's factoring in the risk that confuses me.

Maybe I need to stare at an efficient frontier curve for a while. After all, isn't that the best risk/return tradeoff you can make? Whether it's worth it is a subjective, unquantifiable thing for each individual.

I actually thought it was a simple question:

Investment A has a 10% return, 20% standard deviation.
Investment B has a 5% return, 10% standard deviation.

Clearly, A is riskier. But I was under the illusion that there is an accepted way to quantify the "Risk Adjusted Return" of these two investments.

L.
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Re: Risk Adjusted Return?

Post by Kevin M » Mon Jul 07, 2014 10:07 pm

Leeraar wrote: In your example, I am looking for: We have VG 500 and its return and its risk measure (standard deviation, beta). And, we have Small-Cap Value and its beta. With those three bits of information, can I calculate an expected (risk-adjusted) return for SCV to compare against the actual return? Trying to answer the question, is the extra return worth the extra risk?
Perhaps this will help.

Image
This is from PortfolioVisualizer, and is for 1999-2013; I believe it uses Vanguard small-cap value and 500 index fund for this period.

For a longer perspective, and to see how these things can change over time, here is the efficient frontier from 1972-2013, during which time some other data is used for small-cap value prior to 1999:

Image

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Re: Risk Adjusted Return?

Post by moshe » Mon Jul 07, 2014 10:23 pm

Leeraar wrote:
moshe wrote:
Leeraar wrote:OP here.

I must admit I was surprised to find how much slop there is in the idea of "Risk Adjusted Return", at least for equities. It makes me wonder how the slice and dice / tilting crowd can assess if what they're doing is doing them any good.

L.
Here is what i would do:

RET = (P2-P1+div)/P1

P1 = Initial Outgoing

P2 = End of Period Incoming

div = collected dividends.

RET = % return

Do this calculation for GSPC or VTI and then for your "tilted" portfolio and compare.

~Moshe
Moshe,

I have that part, thank you. It's factoring in the risk that confuses me.

Maybe I need to stare at an efficient frontier curve for a while. After all, isn't that the best risk/return tradeoff you can make? Whether it's worth it is a subjective, unquantifiable thing for each individual.

I actually thought it was a simple question:

Investment A has a 10% return, 20% standard deviation.
Investment B has a 5% return, 10% standard deviation.

Clearly, A is riskier. But I was under the illusion that there is an accepted way to quantify the "Risk Adjusted Return" of these two investments.

L.
Hi L.,

Please note that in my mind there is a major difference between "doing them any good" which would be measured by total return and measuring the risk-adjusted (IOW maximum efficient) return. All the articles and texts i have seen from my pursuit of a finance degree stress, at least so far, the ER(p) from the CAPM model (or fama french if you wish) and using either (or both) the sharpe (excess return/sd) or the treynor (excess return/beta) as a measure of risk adjusted return.

Also, don't forget to get meaningful efficient frontier low correlation results you should be comparing non-similar assets classes. Perhaps use a mixture of BND (total bond market), VXUS (Total foreign market), VNQ (REIT) and VTI (Total US market) for your model portfolio. If you do some regression testing based on different weights you can find some very interesting differences in Sharpe/ Treynor/ Alpha and the information ratio (alpha / standard error).

~Moshe
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Re: Risk Adjusted Return?

Post by Clive » Wed Jul 09, 2014 8:28 am

Time is a factor to consider when assessing risk

For the min, max, average, stdev figures for all UK 1900 onwards 30 year annualised real rewards (where bonds are rolled 20 year gilts (treasury's)), total returns (accumulation/yearly rebalanced) :

Stock/Bonds, min, max, average, stdev

50/50 -0.1% 8.2% 3.7% 1.7%
66/34 0.7% 8.8% 4.4% 1.6%
100/0 2.3% 10.4% 5.8% 1.7%

for the same/similar standard deviation, 100% stocks provided the best worst-case (2.3% 30 year annualised reward).

In the context of 30 year investment periods, 100% stock was the better/safer choice.

If you're investing the proceeds of the sale of a house/home with a view to buying another within the next few months, 100% stocks would be a much riskier choice compared to that of depositing the funds 100% in CD/short term bonds.

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Re: Risk Adjusted Return?

Post by Rodc » Wed Jul 09, 2014 10:41 am

nisiprius wrote:One problem with all measures of risk is "how much data do you need to have to get a valid measurement?" Have you noticed that almost nobody ever talks about this? In ordinary writing, writers simply try to impress you by mentioning how much data has been used, without ever saying how much data would be needed.

I've (finally) been reading Kahneman's "Thinking, Fast and Slow" and was amazed by what he says about what he calls the "law of small numbers." He found that psychologists habitually and consistently plan experiments in which they decide how many trials they need by using their statistical intuition, instead of actually calculating the number--and their intuition is lousy and they very consistently use far too small a number of trials.

Standard deviation itself is bad enough. It takes far more samples to estimate standard deviation accurately than it does to estimate a mean. I've already discovered, if that's the name for it, that "the historic return of the stock market," just the plain old return over the period everyone mentions--1926 to present--can come out as anything from 9% to 11% if you just move the endpoints a few years. The fluctuations are so big that they can influence a sample eight or nine decades long. I ought to try the same exercise with standard deviation, I'll put it on my mental "to-do" list.

Now it's easy enough to say "my personal measure of risk is 'extreme negative events.'" And maybe that can be defended as much more relevant than standard deviation. The problem is that it is far harder to estimate the probability of rare and extreme events than it is to estimate a standard deviation (which is a sort of broad-brush measure of fluctuations of all sizes).
I personally think this is important. And behind my common cautions about using Monte Carlo simulators. If you don't have an decent estimate of the mean, and we don't, and the mean is the easiest parameter to estimate, accurate numerical assessments of return distribution (which includes risk however one wants to define it) are impossible.

So for example this should be rewritten as:
Investment A: 10.99/17.24 = 0.64
Investment B: 5.95 / 9.94 = 0.60
11/17 = .6
6/10 = .6

There is no meaningful difference.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.

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Re: Risk Adjusted Return?

Post by Clive » Wed Jul 09, 2014 11:22 am

Rodc wrote: So for example this should be rewritten as:
Investment A: 10.99/17.24 = 0.64
Investment B: 5.95 / 9.94 = 0.60
11/17 = .6
6/10 = .6

There is no meaningful difference.
Crudely adjusting for the risk-free rate however, perhaps inflation bonds and 3% inflation

(11-3)/17 = 0.47
(6-3)/10 = 0.3

i.e. A has better risk adjusted reward in real (purchase power adjusted) terms.

EDIT - to expand further

Levelled to the same reward :

37.5% of a 11% return with 17 standard deviation, 62.5% of a 3% return with 0% standard deviation has approx ( 0.375 x 11 ) + ( 0.625 x 3 ) = 6% reward with standard deviation of ( 0.375 x 17 ) + ( 0.625 x 0 ) = 6.375.

Which is better than 6% with 10 standard deviation (same average gain with higher volatility = lower reward)

Image
Last edited by Clive on Wed Jul 09, 2014 12:13 pm, edited 1 time in total.

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Re: Risk Adjusted Return?

Post by Rodc » Wed Jul 09, 2014 11:29 am

Clive wrote:
Rodc wrote: So for example this should be rewritten as:
Investment A: 10.99/17.24 = 0.64
Investment B: 5.95 / 9.94 = 0.60
11/17 = .6
6/10 = .6

There is no meaningful difference.
Crudely adjusting for the risk-free rate however, perhaps inflation bonds and 3% inflation

(11-3)/17 = 0.47
(6-3)/10 = 0.3

i.e. A has better risk adjusted reward in real (purchase power adjusted) terms.
Fair enough.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.

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Higher mathematics ?

Post by Taylor Larimore » Wed Jul 09, 2014 2:03 pm

Bogleheads:

I wonder how many of us understand higher mathematics skills? I don't, and I was Chief of the Financial Division of SBA (S. Florida).

Perhaps a better question is: Does in-depth analysis of past performance help us be better investors?

Best wishes.
Taylor
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Re: Higher mathematics ?

Post by moshe » Wed Jul 09, 2014 4:06 pm

Taylor Larimore wrote:Bogleheads:

I wonder how many of us understand higher mathematics skills? I don't, and I was Chief of the Financial Division of SBA (S. Florida).

Perhaps a better question is: Does in-depth analysis of past performance help us be better investors?

Best wishes.
Taylor
Taylor hi,

Speaking for myself i would say yes. Now i understand and can prove why diversification is a good idea. I can also measure total return and can compare returns with or without dividend reinvestment. I can also estimate if my asset allocation generates/generated any market exceeding "alpha".

As a result i expect to:
1) increase my risk adjusted returns over time.
2) enjoy investing and laughing at the " sky is falling talking heads" on the financial channels/marketwatch/etc.
3) sleep better.

All this seems to me like a worthwhile investment of my time and effort to understand today what i did not yesterday. This pursuit of understanding is my personal "alpha".

~Moshe
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Re: Risk Adjusted Return?

Post by Tanelorn » Wed Jul 09, 2014 4:36 pm

Sharpe ratio is a good first pass at assessing risk-adjusted return. After that, it's worth looking into the correlation of returns between these A and B strategies and the other major (stock, bond) markets. Something with a low or negative correlation would be attractive even if it had a lower Sharpe ratio than stocks or bonds (the latter are about 0.3, for reference). If the correlation was high to either stocks or bonds, then comparing the Sharpe ratio to that major market is a pretty good test for how good one is relative to the other.

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Re: Risk Adjusted Return?

Post by Clive » Wed Jul 09, 2014 4:47 pm

Tanelorn wrote:it's worth looking into the correlation of returns
Correlations (and volatility) are as equally variable/unpredictable as price changes.

i.e. you can employ long/short strategies to potentially gain (or lose) from correlations, or trade Options to target volatility.

There are the obvious consistent cases, such as being long DOW, short DOG. But in order to profit you need two assets both with positive reward expectancy.

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Re: Risk Adjusted Return?

Post by Tanelorn » Wed Jul 09, 2014 11:42 pm

Clive wrote:
Tanelorn wrote:it's worth looking into the correlation of returns
Correlations (and volatility) are as equally variable/unpredictable as price changes.

i.e. you can employ long/short strategies to potentially gain (or lose) from correlations, or trade Options to target volatility.
Like price changes, correlations can only observed/sampled and you can never know the true value of a statistical process. Still, people buy stocks based on their long term average returns and similarly it's worth something to look at correlations, however imperfectly measured or indicative of the future.

Depending on the nature of the strategies, it may be hard to bet on their correlations or volatility directly. However, these are still useful factors in portfolio construction and asset allocation.

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Re: Risk Adjusted Return?

Post by Clive » Thu Jul 10, 2014 3:46 am

it's worth something to look at correlations
All knowledge is generally good - but a little knowledge can be bad, such as luring you into a false sense of security where otherwise you might not have ventured.

You're better placed being aware of the variations in measures across time. Long dated treasury bonds for instance can be negatively correlated to stocks over short periods, but not always so, and the two tend to be more positively correlated (but with bonds generally rewarding less) over the mid/longer term.

Often measures are made across relatively short periods (year or less), the individual measures averaged, and those averages used as a basis for investing for longer periods (perhaps 30 retirement years). Only to find that over 30 year periods the expectations/assumptions derived from the measures let you down.

As a example, the Permanent Portfolio 4x25 (stocks, long dated treasury, t-bills, precious metals) has generally provided relatively stable portfolio growth over relatively short periods of time, but becomes riskier over longer periods of time (30 year periods of losing half the portfolio value). For stocks, its the complete opposite (risky over shorter periods, less risky over longer periods (doubles over 30 year periods)).

Single unexpected large outlier events also can result in drift from expectations based on averaging measures. If in a village the average height of a group of 20 individuals is 5', but one of those stands 7' tall, then the average = 5.1' a 2% deviation from the median. You might not find another 7-footer across the remainder of the village population - and may have to wait another century or more before another is found. Such rarer outlier events can often be attributed to the overall longer term outcome. Japan for instance has since 1990 endured repeated bad events either due to domestic cases (1990's crash following 1980's boom, nuclear accident) or global cases (dot com bubble burst, 2008/9 financial crisis). i.e. longer term stock rewards can be more a case of infrequent sizeable steps interspaced with more prolonged periods of plateaus

Generally investments that include modest/sizeable allocations to stocks are longer term investments. Often you'll see models that are based on 10 or 15 year periods being used to argue that one choice is better than another. Yet the longer term for many investors might be 30 years or more of investment lifetime and its much rarer to have multiple/distinct 30 year averages/correlations etc data being made available - often because such length of data is unavailable. And even when available the circumstances of the individual 30 year periods can be distinctly different to the extent that its pointless to even bother to include the data.

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Re: Risk Adjusted Return?

Post by Clive » Thu Jul 10, 2014 4:26 am

Leeraar wrote: Investment A: 10.99/17.24 = 0.64
Investment B: 5.95 / 9.94 = 0.60

So, investment A is slightly less risky. Am I on the right track?
Investment A GENERALLY (over that period) indicated a better risk-adjusted reward.

That's a very general measure however. More commonly risk takes many forms.

Investors typically invest money that they have no need to spend today with a view of spending that money at a later date. One risk therefore is that the money will have lost purchase power between the time of investing the money and the time the money is actually spent, and within that there are taxation/cost risks etc. to also be considered.

Investment A on average provided the higher reward, so had less risk of losing purchase power. But that average gain came with higher volatility, such that for periods within that investment period it was at greater risk of having performed poorly. Taking 2 standard deviations (2x17=34) above and below the average (11) = -23% to +45% range. A relatively unlucky choice of start and end dates (peak to trough) might have resulted in a -23% (equally a lucky choice of start/end dates (trough to peak) might have resulted in a +45%). Average -23 and +45 = 11.

Investment B's 6% average with 10 standard deviation, with 2 standard deviation has a range -14% and +26% (average 6%). A smaller bad case loss risk.

Each of the two can be considered as being less (or more) risky than the other - depending upon what you consider risk to be. As different investors are conscious of different risks, a generalisation is to measure risk-adjusted reward

Average gain less risk-free rate, divided by the deviation/volatility around that average gain.

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Re: Risk Adjusted Return?

Post by Kevin M » Thu Jul 10, 2014 4:22 pm

Clive wrote:<snip>For stocks, its the complete opposite (risky over shorter periods, less risky over longer periods<snip>.
Many would say that this is not true. Once again, it depends how you define risk.

Although it has flaws, my starting point is that risk is uncertainty of return over the relevant holding period. For a holding period of 30 years, the uncertainty of return over one-year holding periods is not relevant from a purely rational point of view (not considering emotional reactions to shorter-term volatility). I'm interested in the uncertainty of return over my 30-year holding period.

Although I'm interested in the uncertainty of my future return, even looking at historical returns shows that the dispersion of stock returns for 30-year holding periods is huge. So a better measure of risk for longer holding periods might be the standard deviation of terminal wealth dispersion.

Although the long-term expected return for stocks is higher than for safe fixed income, so is the variance of terminal wealth. Here is a paper that discusses the trade-offs of expected return and variance of terminal wealth for portfolios of stocks and bonds: Measuring and Controlling Shortfall Risk in Retirement.

Another argument is that if stocks were less risky in the long term, it would cost less to insure against stocks earning less than the risk free rate over longer time periods. Zvi Bodie has shown that this is not the case: ON THE RISK OF STOCKS IN THE LONG RUN.

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Re: Risk Adjusted Return?

Post by Clive » Thu Jul 10, 2014 5:21 pm

Kevin M wrote:Although the long-term expected return for stocks is higher than for safe fixed income, so is the variance of terminal wealth. Here is a paper that discusses the trade-offs of expected return and variance of terminal wealth for portfolios of stocks and bonds: Measuring and Controlling Shortfall Risk in Retirement.

Another argument is that if stocks were less risky in the long term, it would cost less to insure against stocks earning less than the risk free rate over longer time periods. Zvi Bodie has shown that this is not the case: ON THE RISK OF STOCKS IN THE LONG RUN.

Kevin
Thanks for those two links Kevin. I've only skimmed them so far, but will read them in more detail later.

UK 1900 onwards accumulation (dividends reinvested), yearly granularity, 30 year annualised real gains

100% stock

Min 2.3%
Max 10.4%
Average 5.8%
Stdev 1.7%


50/50 stock/bonds (rolled 20 year gilts (treasury bonds))

Min -0.1%
Max 8.2%
Average 3.7%
Stdev 1.7%

It would appear that bonds didn't reduce volatility risk (1.7 stdev in 30 year annualised real gains for both 50/50 and 100% stock) and induced some additional reward risk (-0.1% worst case 30 year annualised real for 50/50 compared to +2.3% for 100% stock).

Perhaps the Options based cost of insurance for 30 year periods is too expensive (better to sell such insurance than buy insurance).

Jeremy Siegel has published a chart that indicates 30 year annualised real US stock returns 1901 - 2000 that generally appears to be similar to that of the UK distribution (I don't however have average, stdev, min/max figures for such).

There's been some pretty good and pretty bad periods/events over the last 100 odd years - perhaps both the UK and US might have been outlier cases? Looking more widely across a range of other markets long term (1900 onwards) :

http://monevator.com/world-stock-markets-data/ Long term returns from different countries’ stock markets (Annualized real returns)

Australia 7.4%
Austria 0.7%
Belgium 2.6%
Canada 5.7%
Denmark 5.2%
Finland 5.3%
France 3.2%
Germany 3.2%
Ireland 4.1%
Italy 1.9%
Japan 4.1%
Netherlands 4.9%
N. Zealand 6.0%
Norway 4.3%
Portugal 3.7%
S. Africa 7.4%
Spain 3.6%
Sweden 5.8%
Switzerland 4.4%
U.K. 5.3%
U.S.A. 6.5%
World 5.2%

indicates that both the US and UK were pretty typical rather than outliers. Australia and Africa were more the outliers on the positive side, Austria and Italy outliers on the negative side. Globally diversifying (equal weighted) and settling for the average would reduce single market risk (such as Japan since 1990).

If I assume a worst case 2.3% 30 year annualised real stock accumulation reward, then 50% in a 30 year inflation bond ladder = 1.66% yearly drawdowns and 50% in stocks that grow 2.3% annualised real doubles over 30 years - in which case you average 75% stock over the 30 year period (start with 50% in stocks, end with 100% in stocks). In the (better) average case you average >75% stock - or you can top slice/profit take additional periodic lump sums/income. Average 30 year annualised for UK was 5.8% less 2.3% min leaves 3.5% potential top slice 'surplus' and with 75% average stock = 3.5 x 0.75 = 2.625%/year typically. 1.66% from inflation bonds drawdown, 2.6% from top slicing from stocks = 4.3%/year 'income', inflation adjusted and with reasonable prospect of ending 30 years with a similar inflation adjusted amount as at the start - for the average case. 1.7%/year income for a bad 30 year period.

If you're content to drawdown (to zero) rather than leave a comparable inflation adjusted amount at the end of 30 years as at the start of the 30 years, then income would be relatively higher (typically 3.3%/year more).

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Kevin M
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Re: Risk Adjusted Return?

Post by Kevin M » Thu Jul 10, 2014 6:32 pm

Clive,

Assuming returns are normally distributed and that that returns in different years are uncorrelated with each other, variance of total (cumulative) return grows linearly (i.e., number of years x annual variance) and standard deviation grows at annual SD x sqrt(n). Stocks generally have higher variance of one-year returns than bonds, so have even higher variance of total return over longer time periods.

Another way this sometimes is described is that although the probability of poor returns decreases over time, the magnitude of the low-probability losses increases over time. Risk averse investors should consider the magnitude as well as the probability of poor returns. The future may not resemble the past.

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Clive
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Re: Risk Adjusted Return?

Post by Clive » Thu Jul 10, 2014 7:28 pm

After a quick browse through Zvi Bodie's paper it looks to me to be (with greatest of respect) a brain-accident.

From Table 1 of the paper, 1 year cost to insure a risk-free return = 8% (rounding). Stocks are renown for being volatile over the shorter term with single year declines of -20% or more being relatively common. Generally for the longer term you might expect to pay a premium equivalent to the risk-premium to ensure that you achieved at least the risk-free rate. Better still, don't invest in stocks, just deposit the funds in a risk-free asset and earn the risk-free rate. However, assuming you prefer the invest in stocks and pay insurance approach then if the risk-premium for stocks is 4%, then expect to pay that in insurance to ensure a risk-free rate of return.

8% cost for one year insurance, 4%/year for longer term, and that's a relatively lower cost the longer the term - not a increasing cost the longer the term.

Summing all yearly insurance payments into a single up-front amount is a odd choice of approach. Whilst that reveals a increasing total insurance cost the longer the term, to then use that positive sloping progression as a argument that insurance costs relatively more over longer periods is creative.
the probability of poor returns decreases over time, the magnitude of the low-probability losses increases over time.
For single stock risk - taken to an extreme and the risk of a total (large) loss becomes more likely (everything dies sooner or later). For a portfolio of stocks however ??? A diversified portfolio is more tolerant to a few individuals dying relatively frequently, replacing such with new blood. The risk of an index of stocks totally failing is much more remote, but whilst that can still happen, holding a global bunch of indexes reduces that risk to insignificant.
standard deviation grows at annual SD x sqrt(n)
and diversification is also a sqrt(n) function (some single stock investors suggest you don't get much more diversification benefit beyond 30 stocks i.e. Dow 30 isn't particularly any riskier than S&P 500).

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Re: Risk Adjusted Return?

Post by Kevin M » Thu Jul 10, 2014 8:55 pm

Clive wrote: and diversification is also a sqrt(n) function (some single stock investors suggest you don't get much more diversification benefit beyond 30 stocks i.e. Dow 30 isn't particularly any riskier than S&P 500).
That argument has been debunked. Here is one example by Boglehead author Bill Bernstein: The 15-Stock Diversification Myth.

Now if you are using only 30 megacap stocks like those in the Dow, then you're likely to track a large-cap US index with many more stocks, like the S&P 500, since the total market cap of the Dow stocks represents a pretty good chunk of the total market cap of the S&P 500, but that's getting us off on a tangent.

Regarding Zvi Bodie's brain fart, Bodie is a highly respected academic economist. He is the co-author of one of the most widely used investment textbooks, "Investments" (also used in the certification programs of the CFA Institute and the Society of Actuaries), as well as the highly respected textbooks "Finance" and "Financial Economics" (co-authored with Nobel prize winner Robert Merton). He understands portfolio theory more than most of us, so although I'd be interested in any peer-reviewed academic articles that present a coherent criticism of his option pricing argument, any argument that starts out by accusing him of a brain fart doesn't have much credibility.

To say that stocks are not risky over any given time period violates a fundamental principle of portfolio theory: that higher expected return over a given holding period is associated with higher uncertainty.

Even respected Boglehead authors like Bill Bernstein and Larry Swedroe tell us that stocks are risky in the long run. Those with long investment horizons don't invest in stocks because they are not risky, but because that's the only way they are likely to have a shot at a decent retirement (higher probability, but not certainty), and because their larger human capital provides them with more alternatives if things don't work out.

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