What is the best measure of risk for funds?

javier

The following is taken from a book that you can read on-line at: http://www.investment-strategies.com/book/index.htm.

"Risk comes from several sources. Most finance books break it down like this:

Business Risk - A company may fail, leaving the stock or bond you hold worthless. Market Risk - Even if you have a strong company, a declining market may carry your stock down with it. Interest Rate Risk - The value of bonds varies inversely with interest rates. Stocks and other property are also affected by general interest rates. Inflation Risk - Your investment may not keep pace with inflation, resulting in a decrease in wealth or buying power. Currency Risk - Foreign holdings may change in value as the value of currency changes. Political Risk - The government may do something to harm the economic climate. This can vary from raising taxes, revolution, war, or confiscation of property, to imposing a minimum wage. "

the book is well worth reading.

.tim.

Traditional investment risk is defined using standard deviation. This stinks because it measures both up and down movements. When talking about risk, people try to gauge what they would be comfortable with. Would you be uncomfortable with a fund that took huge UPWARD swings - I doubt it. Most people are uncomfortable with large/frequent DOWNWARD moves. There is no real formula to measure this.

If you check out Duff Young's article on Fund Hangovers, it details a couple of funds that are riskier than most people probably think. It measures the biggest drop the fund ever had (whether it took 1 month or 1 year), then tells you how long it took the fund to recover to its previous peak. This is a simple yet powerful measure of risk.

My personal favorite risk measurement tool is All Time Periods (ATP). Read about it at:

I think the Fund Counsel Quotient (FCQ) can be a useful indicator of the risk in buying a fund because it is a reflection of consistency of returns (See article in G&M 6/11/97 or at www.globefund.com). It is calulated by stripping away the best year's performance from a fund's 5yr compound rate of return and recalculating an adjusted four year rate of return. The ratio of the four year value to the five value is a measure of consistency (inverse of risk). If the ratio is 100% a fund is truly consistent, a value of 50% indicates that fund's rate of return would have been 50% lower without it's best year. For more information on this go to the fund counsel web site where FCQ values for 146 mutual funds are listed (www.fundcounsel.com). Hope this is useful.

The issue here is risk. I thinks it's silly to punish a fund for one great year. If you focus on looking at the year-by-year returns, you will see how consistent a funds is. True one great year skews the compound returns - but maybe you shouldn't be looking at compound returns to analyze your funds. Look at individual years. This way you give credit to that one spectacular year - but you only count it once.

I think the guys at Fund Counsel need a little counselling themselves. I don't know how they got a regular Globe column but I just don't trust much of what they advise. And I've heard they carry a different tune in the Globe vs. in their newsletter. "Thank you so much for advising all of us to switch to cash in March of this year. Wonderful call!" Okay, I'll stop. I know there was another thread about these guys...just had to let it out.

Any Fund Counsel's subscribers, could you confirm whether there was any recommendation to move back into the market since March, when a categoric "switch all to cash" was issued?

ONTARIO FA, re: punishing a fund gor a great year - if you look at compound annual rate of return together with SD, it makes sense. That one great year would push the CARR higher, but the higher SD would warn you that this is not always the case. By definition, an average rate is somewhere in the middle, so you would always have better years and worse years. OTOH, I agree with you that annual figures are more useful.

Javier - i'm not a professional, just a do-it-yourselfer.

Like Ontario FA, I like to study the funds yearly returns (Jan 1 to Dec 31) rather than the compound numbers and compare them to the mean of their subgroup. In addition, the beta numbers give some indication of how the fund will do against the market index. And finally, especially in these uncertain times, I look at the price/earnings ratio of all the stocks in a fund's portfolio.

Personally I feel that there is no need to be concerned about risk. Risk is so relative. I think that people should get to know the companies within a fund. Dig down to the core holdings, the top 10, and then investigate them. Now a company like Coke is not going to roll over and die overnight. It is a solid company. People should also try to buy companies that produce some of the products or services that they themselves use. Take Johnston 'n Johnston, Gillette, Proctor and Gamble. These are good solid companies. Yes if you want to be a little more risky you can go with the lesser-known companies, but still you should do some homework. Remember you wouldn't buy a car without a test drive or a pig in a bag. You need to test things out.

Just an amateurs opinion, please be gentle.

DJ,

I seem to remember the same comments made about IBM a few years ago - you know, the "grandmother's stock"? The same one that cost people BIG $$$$$!!!

Risk is real, and it's something that needs to be managed. It can be managed using the basic principles talked about by most of the experienced investors on this site (both FPs and DIYs)

My reservations about the fund counsel's method - dropping the best yr of a five yr period - is that it provides a skewed view of performance. Eliminating the upper outlier reduces the probability of one really good year skewing the compounded returns. But by not eliminating the bottom outlier they are presenting an unbalanced picture of a fund's performance level. For balance they should exclude the best and worst years of a five yr period in determining their quotient measurement. In the same vein, one very bad year can also negatively skew one's impression of a fund's overall performance by dragging down the compound return.

I see little advantage with their quotient measurement. There is no better unbiased depiction of volatility than variance or standard deviation. And I remain doubtful there ever will.

Risk is in the eyes of the beholder. Know your own objectives and just worry about that.

I will not try to attempt to define risk, as I think it is different to everyone. But's here's my down-to-earth opinion in understandable language for newer investors.

Similar to some of what's been said already, look at what the fund owns, and see if you like it. The more names that you haven't heard of, the more risk it will carry (especially if you're looking at a Cdn equity fund; this may not apply the same in a foreign fund, unless you are familiar with names of companies in the area they are investing).

And look at the high and low of the price for that fund (NAPVS) over the past year. Say the high is $20 and the low is $10. If you want to buy it at $20, then you're probably looking at more risk than than buying a similar one at $15. If you can't take the fund dropping from $20 down to $10 (and possibly lower), then the risk is too high for you.

The preceding also has to do with volatility. I believe the same thing applies to stocks as well as funds, in most cases as well.

This is keeping it simple, but I believe is also logical for most people. Especially if they don't have the knowledge or access to fundamental information, and don't have the urge to analyze things.

Standard deviation is what it is - namely a measure of the average variability of a list of numbers (here rates of return) from the mean. The phrase "central tendency" is usually used in stats texts, and it's a good one - especially compared to the word risk.

I agree that calendar year returns are very useful, however, I think TRAILING RETURNS are even better as you look at many more different reporting periods, which can expose risky funds and how relatively volatile even some "plain Jane" equity funds are. e.g. Trimark Canadian has a 5year trailing returns of (best,worst,average): 26.8, 5.1, 12.7.

A PalTrak bar graph makes a compelling case for DCAing any lump sums you may stumble across. It will just increase the probability of getting an average return for that fund.

Well now, gotta say thet we got two funds here:
A has got itself returns which oscillated between 30% and 50% over the past umpteen years 'n' B which done did 'xactly the same oscillatin', but 40% lower ... like, between -10% and +10%.

Well now young fellers, use yer fancy risk measures 'n' tell us-all:
Which is the riskier^*?

^*: Y'all 'mediately see thet they both got themselves the same Standard Deviation, no?

Gummy, thank you for your message. Could you tell me how can I obtain info on the ATP?. You can contact directly with me, by my e-mail, if you want to.

I think risk is something that should be viewed form different angles. What I mean by this is a compilation of different measurements including beta, standard deviation, Sharpe and Treynor measurement. One should also look at Trailing performance already mentioned. I believe that utlizing various measurements, especially when ranking a group of funds, is key in painting a much more precise picture.Standard deviation will always be one of the key measurements in determing volatility.

Please excuse my vocabulary, I'm only on my first coffee.

My favourite disclaimer: "Past performance is not necessarily indicative of future returns". Does this apply to volatility as well as returns?

Intuitively, we feel that volatility and risk are more predictable than returns. But has anyone seen objective evidence of this?

Randy.

Bart: Could you explain to me the Treynor formula. Thanks a lot.

A has got itself returns which oscillated between 30% and 50% over the past umpteen years 'n' B which done did 'xactly the same oscillatin', but 40% lower ... like, between -10% and +10%.

Well now young fellers, use yer fancy risk measures 'n' tell us-all: Which is the riskier*?

They are identical ito risk, but asset A has a mean return of 40% while asset B has a mean 0% return. Clearly the latter is more desirable in accordance with the risk-return tradeoff associated with investment in risky outcomes.

Two assets with identical risk/std dev's makes the optimal asset choice decision relatively easy. Since risk is independent of asset choice (it is fixed), choice is based solely on the asset yielding the higer return. Under normal circumstances optimal asset choice is based on both risk and return.

Randy. RE: My favourite disclaimer: "Past performance is not necessarily indicative of future returns". Does this apply to volatility as well as returns?

Right on! BOTH historical returns and standard deviation figures are based on NAVPS+distributions, so of course they are both only NECESSARILY accurate of that which has gone by.

gummy. Exactly my point (and thank ya plenty fur 'spressin' it more clearly), standard deviation only indicates the probability (or chance) of finding results deviating from the average (mean) result. A fund that returned a -10% return every time would have a S.D. of 0, as would a fund that returned +10% every time.

So give me a trailing returns graph (the same as ATP, isn't it?) and I'll use my eyes and brain and gut to help me decide. My only concern is that this makes it hard to use the "sort" function to separate the wheat from the chaff with 1400 mutual funds.

javier,

For an explanation of ATP go to the link to Altamira's website that gummy posted earlier in this thread.

I've been playing with the monthly returns for various world markets from Jan, 1975 to June, 1997 and find a number of interesting things I'd like to share (sort of connected to the topic of this thread):

Did you know that:

1. There was not a single 2-year period where you would have lost money in the U.S. Large Cap market.
2. The chances of losing money in European Large Caps was only about 30% of the chance of making more than 10% ... over any 3-year period.
3. In Cdn Small Caps, you were 1 1/2 times more likely to make more than 10% annual return over any 12 month period than to make less than 0%.
4. In Pacific Large Caps, you would have lost more than 5% of your investment over a 6-month period 45% as many times as you would have made money.
   

Consider the following:
There are 246 intervals of length M=24 months (from Jan, 1975 to June, 1997).
You invest in Stock XYZ or perhaps MutualFund ABC.

• What fraction of these 246 24-month intervals would have given you an annual return greater than U = 10%? (U stands for Upper.) Suppose the answer is .5 meaning 50% these intervals would have given you an annual return greater than U = 10%).
• What fraction of these 246 24-month intervals would have given you an annual return of less than L = 0%? (L stands for Lower.) Suppose the answer is .1 meaning 10% of these intervals would have given you an annual return less than L = 0%.

The ratio GR³ = (fraction over 10%)/(fraction under 0%) = .5/.1 = 5 means that you were 5 times more likely to achieve a return of 10% or greater than to make less than 0%.

What if GR³ = 2? Twice as likely to achieve 10% than to lose money.
In fact, for Canadian Large Caps, we have GR³ = 2.0 and for other markets we have the following values of GR³:

 Cdn Large  Cap 2.0
 Cdn Small  Cap 1.5
 U.S. Large Cap 4.9
 U.S. Small Cap 7.6
 Euro Large Cap 3.2
 Asia Large Cap 1.7
 

Of course, GR³ depends upon the values of M, U and L (as well as the total time interval Jan/75 - Jun/97, of course).
We'll call it GR³(M,U,L) so that, since the above list considered the case M = 24 months and more than U = 10% and less than L = 0%, then we're talking about GR³(24,10,0) and from the above list we can see that for US Small Caps, GR³(24,10,0) = 7.6 meaning you were 7.6 times more likely to achieve 10% annual return than to lose money, over any 24 month period!

If you've come this far along, you may be interested to know that:

1. GR³(24,0,0) = infinity for the U.S. Large Cap market.
2. GR³(36,10,0) = 3.3 in European Large Caps.
3. GR³(12,10,0) = 1.5 in Cdn Small Caps.
4. GR³(6,0,-5) = 2.2 in Pacific Large Caps.

P.S. For those gallant few who have made it this far, R³ stands for Risk Reward Ratio:
making LESS than 0% is the Risk and
making MORE than 10% is the Reward and
we consider the Ratio
... and you can guess what G stands for.

What about calculating the average of monthly losses, and the number of losses vs gains in a 3 or 5 year period, for each fund?

I'll very much appreciate your comments on that.

Aah, if only I could get my hands on the monthly returns for a host of mutual funds ...

jd:
I say Investment A has returns which oscillated between 30% and 50% over the past umpteen years and B has exactly the same oscillations, but 40% lower ... between -10% and +10% ... each has the SAME Standard Deviation (SD), hence the same "Volatility" (as per definition of this word).

and you say They are identical as to risk

and I say Then "Risk" is an inappropriate word and many have shared my concern over the misuse of this word.

For a given SD (example: investments A and B above) it seems infinitely more reasonable to consider A less "Risky" (although equally "Volatile"). If you take an investment which often loses money and add 40% to the returns, the variations about the Average Return doesn't change (so SD remains constant) BUT the "Risk" surely decreases!

"Very risky, this Fund. Standard Deviation = 10."
"Really? What was the average annual return over the past umpteen years?"
"It doubled every year ... 100% annual return."
"That's risky?"
"Of course! Don't you know anything about investment analysis?"

gummy,

So if I understand the GR³ correctly, the best place to be is in US small caps?!? This is hardly the conventional wisdom.

Could you also list the ATP average return for these categories (if it's not asking too much).

Thanks,
Randy.

Javier, to answer your question about Treynor measurement, it is the average monthly risk premium (fund or index return minus the risk free rate of return - risk free rates are based on the return on short term G.O.C. T-Bills) divided by the fund beta over last x years. If you are comparing a group of similar funds in the same class ie. small caps, you will notice different numbers representing the Treynor measure. The school of thought is the higher the number, the better. However, this is just one measurement and aagain, a compilation of risk measurements should be applied to assess risk on a particular fund.

Randy: The annualized return over the period Jan1 /75 to June 30/97 and the average of all possible 2-year annual returns (over the same period) are given below.

Market	Annualized	Average
CDN SMALL	12.1%	11.6%
CDN LARGE	11.0%	10.5%
US SMALL	17.7%	16.3%
US LARGE	15.1%	13.9%
EURO LARGE	15.1%	14.7%
PACIFIC LARGE	13.8%	15.8%

I should point out that the average of all possible 2-year annual returns means I compute:
the annualized return for the two years starting Jan 1, 1975
the annualized return for the two years starting Feb 1, 1975
the annualized return for the two years starting Mar 1, 1975
etc. etc.
the annualized return for the two years starting July 1, 1995
then I average them.

I can, if you wish, compute the average annual returns over other than 2-years.

Various graphs are available at:

gummy you dummy, you should point out that, in the graphs, the wee rectangles along the horizontal axis are the times when it would have been better to invest all-at-once rather than DCA over the next 10 months. They occur when the market is headin' North!

Thanks gummy (for the graphs too - I had seen them from the other thread).

So from a risk (GR³) and return (average ATP_monthly) perspective, I should have been 100% US Small Cap. Now there's a thought!

Randy.

The danger in comparing small-cap indices to large-cap indices, and assuming that small caps outperform, is that the indices do not reflect companies that fail. It is mostly small-cap companies that go under,and when they do, they are taken off the index, and replaced with another still successful company. I believe that there is more risk and less return in small-caps that any analysis of an index and it's variability would indicate.

Also, gummy, did you know that if you had invested in the S&P 500 in Jan. 1970, your compound annual return to Dec. 1974 would have been -4%. That's 5 years! There is a reason why some publish data that only goes back to 1975.

Madelyn

"It is mostly small-cap companies that go under,and when they do, they are taken off the index, and replaced with another still successful company."

How does this cause the index to overstate the return of small cap funds? This sounds like the same thing I would expect the fund manager to do.

Now, individual campanies... there's a different story.

Randy.

Madelyn: do you know where I can find monthly (or even annual) returns back to the beginning of time (or thereabouts)? I'm limited to the collection I found (with Bylo's help, at Sharpe's site) and they begin in 1975. With all this time on my hands (and my magic spreadsheet) I'd have fun aplenty with more data.

gummy,

I say Investment A has returns which oscillated between 30% and 50% over the past umpteen years and B has exactly the same oscillations, but 40% lower ... between -10% and +10% ... each has the SAME Standard Deviation (SD), hence the same "Volatility" (as per definition of this word). and you say They are identical as to risk and I say Then "Risk" is an inappropriate word and many have shared my concern over the misuse of this word.

Risk is simply not knowing which of different possible outcomes will actually occur at various future dates. It is synonymous with uncertainty. In this context, both assets A and B are identical. They both face identical risk, or dispersion about their mean. Of course, however, asset A is the preferred choice with its higher mean return. You are trying to combine the definitions of return with risk, which is a natural yet incorrect tendency - they are separate.

For a given SD (example: investments A and B above) it seems infinitely more reasonable to consider A less "Risky" (although equally "Volatile"). If you take an investment which often loses money and add 40% to the returns, the variations about the Average Return doesn't change (so SD remains constant)BUT the "Risk" surely decreases!

At the risk of sounding infinitely unreasonable, I disagree. The risk hasn't changed, only the mean return. The risk levels remain unchanged. Asset A is the preferred choice, of course, with it's higher mean, but the risks are identical.

Now consider dividing SD by the Average Annual Return. When the Average Return increases, this ratio decreases. It makes a more reasonable measure of "Risk". The Ratio (SD/Mean Return) is the reciprocal of the Sharpe Ratio.

Not quite. Recall the Sharpe index or "price of risk" is the risk premium divided by the SD,

(r_asset - r_f)/SD
where r_f is a risk-free return.

It is often called the "price of risk" since it measures how risk and return can be traded off in making portfolio choices. I agree with you that the Sharpe Index is a reasonable measure of an asset's efficacy, but it doesn't measure risk alone. The measure combines the characteristics of both risk and return.

It is not a perfect measure, either. Look up in Paltrak the asset with the highest Sharpe Index measure.

Hi Randy, I guess I wasn't clear there. If you look at the Russell 2000, which is the small-cap index most follow in the US, the index is comprised of the smallest 2000 stocks of the Russell 3000, which is the largest 3000 companies domiciled in the US. They are ranked by decreasing market cap.

They exclude companies that trade under $1.00.

So if you look at the companies on the fringe, ...close to the bottom of the 2000, ...on May 31, if they trade under a $1.00, they are removed from the index, and replaced with the lastest company that moved up to a trading range over $1.00.

Looking at the company that was removed, if it went under sometime later, ...that risk is not taken into consideration. Also, if it dropped $.50 on May 31, but recovered within the year, and the next year was trading at $1.50,...& put back in the index, we don't see that fluctuation reflected in the SD of the small-cap index. We just see another company removed that's now trading at under $1.

It has been shown that contrary to the popular stats about fund managers not beating the S&P etc., it is much easier for them to beat the small-cap indexes. I think that these arbitrary rules of inclusion are why this is so. The large-cap indices are not subject to so much change-over.

My main point is that the returns & the risks of small-cap investing cannot be measured correctly by looking at the indices.

Gummy, you want data? I got data for you....Go to http://econwpa.wustl.edu/eprints/data/papers/9603/9603001.abs#viewing

Here you will find Dow DAILY closing prices from 1900 to 1993, and S&P DAILY closings from 1926 to 1993. That ought to keep you busy for awhile.

Nice work you're doing by the way. Glad to see you've seen the light with DCA. Now, what would probably be useful, given the ageing population, is to prove (please!), why SWPs DON'T work. It has been my contention that SWPs don't work for the reasons that DCA does. Common sense tells me this is so, but I honestly haven't done the analysis that you do. Anyway, there's another project for you when you get a minute. ;-)

Madelyn,

I appreciate your explanation of small cap indices. You've made it clear that they do not fully expose the risk. But you also stated that, with small caps, a good manager should beat the index - I assume for both risk and return. So I still find this to be a very intriguing area of investing; maybe worth a larger portion of my portfolio than most analysts would recommend.

Incidently, I've considered, and agree, with your point about SWPs. To the extent that DCA's advantage comes from a level dollar amount, SWPs should only maximize (pretax) return if you withdraw a level number of units. If you're lucky this will mimick your inflated needs over time; but most people do not have flexible enough cash flow requirements to follow through with this. Gummy's analysis would be interesting, but I'm also wondering what your alternative is.

Randy.

WHOOEE!!
Thanks Bylo 'n' Madelyn for the links!
Billions of Bytes
... the entire 20^th century world of investing!
... gotta get off this couch
... uh, can anyone remind me of what SWP means? Somekinda Withdrawal Plan?

jd:
risk, n. & v.t. 1. Hazard, chance of bad consequences, loss, etc. 2. Expose to chance of injury or loss.

It's quite clear ... funds A and B have the same "risk". Right!
(One should ALWAYS change the meaning of a word when practising the art of obfuscation.)

SWP= Systematic Withdrawal Plan

or for the more mathematically re/inclined:

SWP = -DCA

Randy.

Bylo's second-favourite bumper sticker:

The best risk measure for a fund is to sell the best performing fund of last year.

Thanks for the article, Bylo. I actually understood about 80% of it... scary! Here's some of my thoughts on it.

I especially liked the concept that the Sharpe Ratio (return per unit of risk) must be relative to a another alternative (another fund, a benchmark, cash, or the cost of borrowing) because you always go short in one asset to go long in another. I'll have to look through the Paltrak help screens to find out what basis they use for their Sharpe Ratios.

My question is: have you ever actually gone through a calculation like this to determine which investment and how much of it to buy?

Personally, I've been eyeballing it off a (historical) risk/return graph to make selections but that doesn't provide much help in determining allocations (whereas the Sharpe Ratio could).

One disturbing slant to this article is that he seems to prefer the ex ante Sharpe Ratio (based on expected rather than historical returns). I know the standard disclaimer about historical returns, but isn't a calculation based on market forcasts just another forcast with a mathematically amplified margin of error?

The other missing piece, of course, is correlations between markets. Can you point me to any data on this?

Randy.

Randy,

First off, I just noticed that gummy (who else?) already cited Sharpe's paper earlier in this thread. Sorry gummy, I didn't mean to "steal yer thunder."

Two of the best sources for information on investing in mutual funds using a balanced portfolio of poorly correlated asset classes are the online books by Armstrong and Bernstein.