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,