The first problem we faced in calculating the expected returns was whether or not to used a historical average or calculate beta and apply the CAPM. We decided to find beta and calculate the CAPM. The reasoning is that our investor is interested in forecasting future returns. Even though beta is theoretical and largely inaccurate, it is the best tool available to the analyst.

To calculate beta we considered three methods. The first was to look up historical betas for each of the assets. We used Yahoo Finance. The second method was to use the formula; CovRm, RiVarRi and apply it to each of the funds. Lastly, we regressed the monthly returns of each of the assets with the monthly market risk premium to estimate beta (see exhibit 1). For our purposes we valued the covariance formula and the regression analysis more than historical data since we are more interested in forecasting. The output for these methods returned almost identical results for every fund so we used the average of the two as our estimated beta. There were three exceptions – the last three assets (TIDRX, TIKRX, and TIQRX). We felt that there might not have been a large enough sample set to get an accurate result from the same type of analysis, so we defaulted to the historical figures calculated by Yahoo Finance for these three assets.
Next, we considered alpha. We strongly feel that markets are efficient and any estimation of alpha for use to identify under or overvalued assets – in essence to beat the market – is an analytical mistake. Therefore we assumed a zero value for alpha for each fund.

Another problem we faced was whether to use all data included or to achieve consistency in time durations and use only the last four years of data. We decided that the opportunity cost of not using every resource was too great to over look. Thus, we sacrificed consistency and used all the data available for each fund. We also feel that the use of more data (assuming the data is accurate and relevant) in financial analysis returns stronger estimations in general and leads to more accurate forecasting.

The following is the math we used to arrive at our estimates: ERimonthly = βRm-Rf+Rf Where E(Ri) is the monthly estimated return, β is the beta assigned to the specific fund, Rm – Rf is the market risk premium, and Rf is the risk free rate. After acquiring E(Ri) for each month, we found the monthly average then multiplied the result by 10 months.

Our estimated returns for the 10 months remaining in 2011 are as follows:

TRBIX | TRGMX | TRIEX | TRLCX | TRRSX | TRSCX | TRSPX | TRVRX | TIDRX | TIKRX | TIQRX | 8.01% | 7.52% | 7.31% | 7.16% | 8.51% | 6.87% | 6.62% | 7.46% | 1.83% | 1.81% | 1.82% |