# Rate of return, variance and beta for TIAA-CREF funds

I think this may be of interest to others as well as to me, and I hope somebody can help me with it.

Like many other ESPlanner users (I suspect), I have 403(b) funds in TIAA-CREF, and want to do Monte Carlo forecasting with ESPlanner Plus. Specifically, I can invest in any of the first nine funds listed at http://www.tiaa-cref.org/performance/retirement/index.html , and want to forecast with a mix of those funds.

Prof. Kotlikoff has given me as an example, that the CREF US/International Equity fund can be approximated by telling ESPlanner that 60% of any accumulation in that fund is in the built-in large caps fund, 25% in the built-in European equity fund, and 15% in the built-in Pacific Basin fund.

But I can find no way to figure out similar approximations for other eight funds, so I want to try the alternative approach with ESPlanner Plus: entering the rate of return, variance, and beta for each of the funds in which I have an accumulation. The “interesting” part is finding the values to enter.

From http://www.tiaa-cref.org/performance/retirement/data/index.html I downloaded into Excel the daily closing prices for the last 15 years (or since inception if the fund began fewer than 15 years ago.)

I also downloaded 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 the daily closing prices for the S&P 500 for the past 15 years.

For each TIAA-CREF fund and for the S&P index, I calculated

the daily rates of returns for all closing prices using r=(PriceToday/PriceYesterday)-1.

the variance of the returns for each fund and for the S&P index with the Excel VAR function.

the betas for the returns using COVAR(FundReturns, s&pReturns)/VAR(s&pReturns), where COVAR is the Excel covariance function.

the annual rate of return for each fund with (PriceToday/Price15YearsAgo)^(1/15)-1. For funds less than 15 years old, I used the same formula with the age of the fund in place of 15.

VAR(FundReturns)/VAR(s&pReturns), because that’s what ESPlanner requires for the variance entry.

Here are the values I got:
TIAA/CREF fund, years, beta, var, var/varS&P, return
Stock 15, 0.870, 8.65E-06, 0.0235, 10.2
Equity index 13, 0.983, 0.000390, 1.06, 11.0
Real estate 9, 0.0176, 6.08E-07, 0.00165, 12.7
Social choice 15, 0.579, 0.000126, 0.342, 9.0
Bond market 15, -0.0151, 5.89E-06, 0.0160, 6.2
Global equities 15, 0.693, 0.000199, 0.541, 10.0
Inflation linked bonds 6, -0.0383, 8.65E-06, 0.0235, 11.6
Money market 15, 0.000271, 1.56E-08, 4.24E-05, 4.0
Growth 12, 1.131, 5.34E-04, 1.45, 9.0
S&P 15 years, var=0.000368

I’m posting these values for two reasons. First, if they’re correct, others may find them useful. Second, I hope somebody–preferably somebody who knows a heck of a lot more about this stuff than I do–has figured out these values and can either confirm my calculations or tell me where I went wrong. For example, I read that you can estimate beta with daily, weekly, monthly, or annual returns. But ESPlanner deals only with whole years, so using the variance in daily rates for the fund as a fraction of the variance in daily rates for the S&P 500 will work only if that ratio can be expected to be close to the ratio based on annual returns.

Thanks for any help you can give me,

Elbert[/]

1

Hi, Elbert-

I also have funds in TIAA-CREF. I did an appointment with them in order to get a breakout of the different asset categories. The document they sent me included pie charts with percentages in asset classes such as large cap, midcap, international equity, bond funds, TIPS. REIT, and cash that I could put into my Monte Carlo ratios.

The one piece that has been more problematic is with the TIAA Traditional. For that, I went to the tiaacref.org site and figured out what the annuity payment would be with the Standard method and put it in the Pension and Annuities tab. So, the funds included in the Traditional are not part of my Monte Carlo calculations.

I also had to figure the amount of the annual contributions that went to the Traditional fund and put that figure in the Special expenditures to identify it as income that would be tax deferred.

But, if you or anyone else has a sense of how to enter the TIAA Traditional fund in Monte Carlo, I would love to learn about that.

Terry

2

Hi Terry,

Quote:The document they sent me

Wow! Just what I need. Could you let me know the name of that document? I'll ask them to send me one, too.

Thanks,

Elbert

3

I scheduled one of the face-to-face appointments when they came to a nearby college, and when you make your appointment at the tiaacref site you indicate that you want to do an assessment of your asset allocation.

At the meeting I held in September, the rep from TIAA-CREF went over my different funds and then could show me the asset allocation pie chart on his computer. He next ordered a copy of it that I got in the mail about three weeks later.

I hope that helps.

4

Thanks again. I'll get in touch with my TIAA-CREF guy and see if he can get the allocations for me.

Elbert

5

HI, I REPLY BELOW IN CAPS. BEST, LARRY

But I can find no way to figure out similar approximations for other eight funds, so I want to try the alternative approach with ESPlanner Plus: entering the rate of return, variance, and beta for each of the funds in which I have an accumulation. The ÃƒÂ¢Ã¢â€šÂ¬Ã…â€œinterestingÃƒÂ¢Ã¢â€šÂ¬Ã‚Â part is finding the values to enter.

THE VARIANCE RATIO YOU NEED TO ENTER IS THE RATIO OF VARIANCE OF THE ANNUAL REAL RETURN ON YOUR NEW ASSET TO THAT ON LARGE CAP STOCKS. THE PERCENTAGE CHANGE IN THE PRICE OF PARTICULAR FUNDS FROM ONE YEAR TO THE NEXT IS ONLY PART OF THE TOTAL RETURN. THERE'S ALSO THE DIVIDEND. YOU ALSO NEED TO ADJUST FOR INFLATION. THE FORMULA FOR THE REAL RETURN OVER THE COURSE OF A YEAR IS ((1+ i)/(1+inf) -1), where i stands for the nominal rate of return on the asset and inf stands for the inflation rate. The nominal rate of return is, in turn, calculated as the (D + P' - P)/P, where D stands for the dividend per share paid out over the course of the year, P stands for the initial share price at the beginning of the year, and P' is the end of year share price.

WE HOPE TO ADD A TOOL TO THE PROGRAM THIS YEAR TO AUTOMATICALLY SHOW USERS HOW THEIR ASSETS FIT INTO OUR 13 CANNED ASSETS.

From http://www.tiaa-cref.org/performance/retirement/data/index.html I downloaded into Excel the daily closing prices for the last 15 years (or since inception if the fund began fewer than 15 years ago.)

I also downloaded 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 the daily closing prices for the S&P 500 for the past 15 years.

For each TIAA-CREF fund and for the S&P index, I calculated

the daily rates of returns for all closing prices using r=(PriceToday/PriceYesterday)-1.

the variance of the returns for each fund and for the S&P index with the Excel VAR function.

the betas for the returns using COVAR(FundReturns, s&pReturns)/VAR(s&pReturns), where COVAR is the Excel covariance function.

the annual rate of return for each fund with (PriceToday/Price15YearsAgo)^(1/15)-1. For funds less than 15 years old, I used the same formula with the age of the fund in place of 15.

VAR(FundReturns)/VAR(s&pReturns), because thatÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢s what ESPlanner requires for the variance entry.

Here are the values I got:
TIAA/CREF fund, years, beta, var, var/varS&P, return
Stock 15, 0.870, 8.65E-06, 0.0235, 10.2
Equity index 13, 0.983, 0.000390, 1.06, 11.0
Real estate 9, 0.0176, 6.08E-07, 0.00165, 12.7
Social choice 15, 0.579, 0.000126, 0.342, 9.0
Bond market 15, -0.0151, 5.89E-06, 0.0160, 6.2
Global equities 15, 0.693, 0.000199, 0.541, 10.0
Inflation linked bonds 6, -0.0383, 8.65E-06, 0.0235, 11.6
Money market 15, 0.000271, 1.56E-08, 4.24E-05, 4.0
Growth 12, 1.131, 5.34E-04, 1.45, 9.0
S&P 15 years, var=0.000368

6

Larry,

Thanks for the reply.

It just keeps getting curiouser and curiouser. It's not that your explanation is unclear, but it seems that every time I manage to understand one thing, something else comes up to stump me. For example, you say I have to use real returns when calculating var(MyFund)/var(LargeCaps), which gets me to wondering whether when I add a new asset I have to specify as the nominal rate of return the real rate or the rate unadjusted for inflation. I dunno. So I guess I'll give up trying to use ESPlanner until I'm able to model my assets in terms of the canned assets.

I hope that I can get the document Terry mentioned, and that I'll be able to fit my funds into ESPlanner's canned assets. I am concerned that I won't know what to do if that document says, for example, that 20% of the fund is in large cap growth and 15% is in large cap value, etc., since neither of those is an ESPlanner canned asset. But I'll try to get it and see.

If I can't get the document or can't figure out how to use it, then I guess I'll wait for the new tool you mention. I'm a little worried about that, too, because I recall reading somewhere that to use the tool, I'll need to enter the ticker symbol for my asset. Since the funds I have available to me are not traded on an exchange and therefore have no ticker symbol, I'm concerned that the tool won't work for me.

Let me repeat my plea that you post in this forum the fits to the canned assets for the nine TIAA-CREF funds. By email, you already told me the fit for the CREF US/International Equity fund, so there are only eight remaining, and I hope providing those breakdowns won't be too time consuming for you. This would be an immediate and tremendous help to me and other members of TIAA-CREF.

7

Back in December, Prof. Kotlikoff said

WE HOPE TO ADD A TOOL TO THE PROGRAM THIS YEAR TO AUTOMATICALLY SHOW USERS HOW THEIR ASSETS FIT INTO OUR 13 CANNED ASSETS.

I've given up trying to use ESPlanner until that program is available, so I thought I'd check in to see if it is yet.

Thanks to anyone who can let me know.

8

Elbert wrote:Back in December, Prof. Kotlikoff said

WE HOPE TO ADD A TOOL TO THE PROGRAM THIS YEAR TO AUTOMATICALLY SHOW USERS HOW THEIR ASSETS FIT INTO OUR 13 CANNED ASSETS.

I've given up trying to use ESPlanner until that program is available, so I thought I'd check in to see if it is yet.

Thanks to anyone who can let me know.
Not yet.

Best,

Dick Munroe

9

Hi,

Any hope of ever seeing this? I'd really like be able to use ESPlanner.

Thanks.

10

I'm a little out of the loop on this one as Larry has been involved in the negotiations with the company who will be providing the data so I can't give a specific answer. We're currently focused on getting web based versions of ESPlanner (initially a very simplified version) into production and that's consuming most of our available resources.

Sorry I can't be more specific.

Best,

Dick Munroe