Creating "New Asset" in Monte Carlo Build Portfoli
Please tell me how to derive the values for "Average Return" and "Risk" if I want to create a new asset in the Monte Carlo "Build Portfolios" screen. I would like to use the same values that the ESPlanner programmers would use if they created the New Asset. For example, if I want to create an "Energy Stock" asset class and plan to use the Vanguard Energy mutual fund (VGENX) as the investment vehicle, where can I find the "Average Return" and "Risk" values that would correspond to what the programmers would use?
RSS
Vanguard should have available the mean rates of return for all their funds. This value would be the rate of return that you would enter. What you need in addition is the variance (a statistical term that I leave to Larry to explain in details) of the real rate of return. The variance is a measure of how "stable" the mean real rate of return is. Assets with large variance have high probablities of either low or high returns in any given year. Assets with small variances have high probabilities of nearly the same rate of return in any given year. Vanguard should be able to provide this number for you as well. If they can't, then they should be able to provide you with the historic returns, year by year, for their funds and a little work with Excel (or a calculator) should give you the variance of the fund of interest (in your case "Energy"). To make things more interesting, the variance (risk) of the mean real rate of return isn't specified as a number, it's specified as a percentage of the variance of Large Cap Stocks (fyi, the variance of large cap stocks is about .0387 at the moment).
Up to version 2.8.3 R3 of ESPlanner the variance of user defined assets was specified relative to large cap stocks (.0387) in fairly large increments (1/3 to 2 by 1/3s). So, say the Energy fund had a variance of .013. In 2.8.3 R3 you would say that the variance of the asset was 1/3 of diversified stocks. Version 2.8.4 improves this by allowing a finer mechanism for controlling the risk (from 2.0 to .2 by .01 as well as the original mechanism).
Hope this helps.
Thanks for the information that ESPlanner provided.
Vanguard, other mutual funds, and Morningstar all provide a "total return" figure for 1 year, 3 years, 5 years, and 10 years. Which time period corresponds to what the ESPlanner programmers would use? Then, is it correct to use that figure as-is, or should inflation be subtracted to provide a calculated "real return" figure?
Also, does the ESPlanner "risk" figure correspond to either the standard deviation or the beta figures that the funds and Morningstar provide? Those two are usually the only figures available. If neither of those is the right thing to use, do you know of another source?
Thanks again.
ESPlanner uses the entire historical average for all defined assets. We go to the source (primarily Ibbotson for stocks/bonds/cash and Morgan Stanley for most other defined assets) and use the entire series. For the classic assets (Large cap stocks, cash, etc) the historical series goes back to the 1920s. For others the series is substantially shorter (Pacific Equities only goes back a few years, for example).
If you don't have access to the entire historical series (back to the founding of the asset you're defining) then use the longest one you have access to. You'll still need to calculate the variance though in order to be able to assign risk relative to large cap stocks.
Thanks for the additional information.
I still need advice on the practical method to use to derive the "risk" figure to enter when creating a new asset. Will either the standard deviation or the beta that is provided for a mutual fund serve that purpose? If not, how can I find or calculate the "risk" figure so that it is the same as what the ESPlanner programmers would use?
These questions raise an important issue. A user needs to be able to create a new asset that functions the same as the standard asset classes in ESPlanner. Otherwise, trying to cusotmize the Monte Carlo simulation to match the user's real-world situation is not possible. That would make ESPlanners' Monte Carlo simulation much less valuable to the user. So please try to help.
Thanks again.
With respect to the risk of new assets, we ask you to enter the ratio of the variance of the new asset you are entering to the variance of large cap stock. We are assuming with respect to new assets that their return is not correlated with that of the canned assets already in the program. We are examining how best to modify this simple assumption to permit users to easily tell us about covariances. Give us a couple of months on this.
Some users have been able to use other programs to determine the variance of their new assets relative to large cap stock. One of our users, Phil Stephenson, suggested using http://www.effisols.com. I haven't checked this out, but will shortly.
best, Larry
PS, call me at 617 834-2148 if what I wrote isn't clear.
Anothe web site with information on portfolio modeling (http://www.quantext.com/subpage.html) is maintained by Quantex. I have not used the product but the articles on portfolio modeling seem useful to the non-professional.
An article there alerted me to the issue of the lack of clear definition of the asset classes in most modeling schemes which means the user is at a loss to figure out how to match their holdings to the model's classes. Even where the modeling program has access to the detailed of holdings (named mutual fund, stock, bond, ETF, etc) different models will give different interpretations of asset allocation (I've done this with Quicken, Fidelity, and Morningstar allocation tools).
How important this is given the other uncertainties in planning I'm not sure.
PMFJI, but I have a related question.
At http://www.tiaa-cref.org/pdf/performance/standard_deviations.pdf I can find the standard deviation of TIAA-CREF funds. I hope that by squaring the standard deviations I can get the variances I need to enter into ESPlanner to define TIAA-CREF funds as new assets for Monte Carlo calculations.
Variances calculated that way range from 0.0000336 for the money market fund to 0.0281 for the stock fund. ESPlanner wants these values entered as a fraction of the variance of diversified stocks, which munroe says earlier in this thread is 0.0387. So I guess I would enter 0.0281/0.0387=0.726 as the variance for the stock fund.
Also, at http://www.tiaa-cref.org/pdf/performance/correlation_matrix_c38534.pdf I can get correlations between TIAA-CREF funds and indexes such as the S&P 500. I seem to recall that the beta required by ESPlanner can be calculated from the correlation coefficient and the standard deviations for the two funds, but if it can, I don't recall how.
I'd really appreciate feedback about whether I'm on the right track with the variances, and whether or not I can figure out the betas for the TIAA-CREF funds.
Thanks.
Elbert wrote:At http://www.tiaa-cref.org/pdf/performance/standard_deviations.pdf I can find the standard deviation of TIAA-CREF funds. I hope that by squaring the standard deviations I can get the variances I need to enter into ESPlanner to define TIAA-CREF funds as new assets for Monte Carlo calculations.
Yes, the variance is the square of the standard deviation (by definition) so you've got that right.
Elbert wrote:Variances calculated that way range from 0.0000336 for the money market fund to 0.0281 for the stock fund. ESPlanner wants these values entered as a fraction of the variance of diversified stocks, which munroe says earlier in this thread is 0.0387. So I guess I would enter 0.0281/0.0387=0.726 as the variance for the stock fund.
Exactly.
Elbert wrote:Also, at http://www.tiaa-cref.org/pdf/performance/correlation_matrix_c38534.pdf I can get correlations between TIAA-CREF funds and indexes such as the S&P 500. I seem to recall that the beta required by ESPlanner can be calculated from the correlation coefficient and the standard deviations for the two funds, but if it can, I don't recall how.
Beta is defined as the ratio of the covariance (don't ask me how to calculate it, I'll leave that to Larry or just fire up Excel and use its covariance function) of the asset and the covariance of large cap stocks (I don't make this stuff up folks). If the fund doesn't provide you with a beta (usually in 1, 5, and 10 year values) you'll have to calculate it for yourself.
Best,
Dick Munroe
Thanks for the feedback.
I'm not following how to calculate beta. As I understand it, covariance is a function of two random variables, say x and y:
cov(x,y)=E[(x-E(x))(y-E(y))]
where E() is the expected value function. So I don't see how you would calculate the covariance of individual random variables, the asset and large cap stocks, to get the ratio you specify. You can calculate cov(x,x), but that turns out to be var(x), which I doubt is what you had in mind.
My books on statistics do not mention beta, but a Google search turned up this formula:
beta(x,y)=cov(x,y)/var(y)
I wonder if this is what you had in mind?
Thanks again for the help.
Elbert wrote:
beta(x,y)=cov(x,y)/var(y)
Yes, you're right, I misspoke in my earlier note.
Best,
Dick Munroe
I'd like to calculate the variance and beta for funds in my retirement plan, for which I need historical values of rate of return.
I can download daily prices for a fund, but I'm not sure how to calculate the rate of return from the prices. I notice that there are roughly 250 trading days per year. One way would be to calculate for each day the return for one day and then annualize that rate:
Annual rate=[Price(today)/Price(yesterday)]^250-1
Another would be to compare the price each day with the price a year before that day:
Annual rate=Price(today)/Price(250 trading days ago)-1
I probably haven't even thought of the correct way. I hope somebody can tell me how these rates should be calculated for the ultimate purpose of calculating beta.
Thanks for any advice.
Elbert:
The best way that I've seen is to use Yahoo Finance or Morningstar to look up the average annual rate of return for the fund. Use the longest period they have available. You may be able to get the longest data from the fund company itself. The beta is also listed on these sites. The variance relative to large caps is a bit harder since that number is not reported by any of these finance web sites. The standard deviation is, however, always reported. The variance is the standard deviation squared. I assume that you should square the SD of the same time period that you have the return for. And then, you must calculate the relative variance to the same period for large cap stocks. I believe they are considering putting up an online calculator to make this easier, but I'm not sure.
Dan
Thanks, Dan. I haven't been able to find TIAA-CREF retirement funds (as opposed to their mutual funds) in Yahoo or other sources I've tried. I'll look again, but if you know of a source for them, I'd appreciate hearing what it is.
Thanks again,
Elbert
Yes, I think they are there on the TIAA website:
http://www.tiaa-cref.org/performance/retirement/index.html
I don't know if they show the Standard Deviation or the beta though. They might. If you know the ticker on the mutual fund, those are easy on Yahoo Finance (along with beta and SD).
Dan
Thanks for the suggestions.
At http://www.tiaa-cref.org/pdf/performance/standard_deviations.pdf there are standard deviations based on the past 10 years. But I can find no betas at the TIAA site.
At http://www.tiaa-cref.org/performance/retirement/data/index.html I can download prices for 15 years and from
http://finance.yahoo.com/q/hp?s=^GSPC&a=10&b=19&c=1992&d=10&e=19&f=2007&g=d&z=66&y=0
I can get the same 15 years for the S&P500. From those 15 years of data I had hoped to be able to calculate both the variance of the TIAA fund and its beta relative to the S&P numbers. To do that, I have to be able to calculate rate of return from the price data, and I don't know how economists do that.
It may be that the beta isn't very important to the calculations (the instructions do say that if you think your asset is uncorrelated with large cap stocks you can set beta to zero). And it may be that variances based on 10 years are rather than 15 are good enough. So maybe I could just look up the 10 year standard deviations, square them to get the variances, and set the betas to zero. But I understand so little of this stuff that I can't confidently make that decision, so I'm trying to get the best numbers I can.
Thanks again,
Elbert