Hi. I am a bit confused in testing the APT model. Many research papers don't explicitly explain the methodology for APT. What I understood is that,
1) Select macro factors, choose the equities and create the portfolio. Then we need to find the return on each of these stocks over the selected period of time according to the prespecified frequency. Also, we find the risk premiums for the macro factor in this stage (but i am not sure here, do we need to do that) by subtracting the risk free rate from each macro factor's return.
2) We conduct time series regressions of each stock's return on the corresponding variables (so that one regression for each stock) , i.e. risk premiums (or just returns on macro factors?). As a result, we get the intercepts and betas for each stock.
3) Find the average return for each stock over the chosen period. Then do a one cross sectional regression of average returns of the stocks in the portfolio on the betas (factor sensitivities) found in time series regression in step 2.
As a result, we get lambdas(or gammas, up to you), which are the estimates we need, and also the intercept (will it be the risk free rate? If it is negative value, then is it possible to have negative risk free rate?).
4) Finally, we can use the last output (gammas and thee intercept) from the cross sectional regression to construct APT model and estimate the "fair return" on each stock in the given portfolio. After, identify which stock in the portfolio is overvalued or undervalued and make a decision.
Is my understanding here right? If there is misunderstanding or incorrect statements, please let me know. Thanks a lot.
have you run the analysis already? i think you should simply run the analysis. you are going to answer a lot of your questions yourself. you will quickly discover what works and why
Yes, I have run regression. It seems to work, but not as I expected. I mean, prediction is not accurate to say that it is a good model, although the r-squared and r-adjusted are around 0.45 and 0.4 respectively.
is it due to how you have calculated the premiums?
do you have an explanation why it is poor in forecasting?
I have calculated the risk premiums and the overall regression following the Roll and Ross (1980) method. Possible explanations may be that my portfolio selection was not done accurately to diversify the idiosyncratic risk almost completely, because it is one of the most important APT assumptions. In my case, I have chosen only 14 representative companies from the major sectors, which I suppose is not enough to say that the distribution is normal. Frequency of the data was quarterly returns over 1999-2017 years. So, I assume, there shouldn't be problem in the time series regression. Probably, the issue is connected with the numbers of companies in the portfolio, which was not enough for the cross sectional regression.
it would be great if you can adapt the APT model slightly so that the number of issues is less of a concern. i think this should be possible. you would be steering towards a more custom model. at the same time, arbitrage is a common concept in finance, and i would not call it unique to APT per se.
what is you overall objective? to better understand APT? in that case, i think you have accomplished your task. or is it to develop/ have a model to price specific securities? you may be able to 'strip' APT. the objective of APT seems to be to flag overpriced/ underpriced securities. there are a number of ways this can be approached i would think. it seems APT uses a portfolio to evaluate the risk-level of a security.
Sorry for my late answer, Mr. Barnard. Actually, I had a quite different understanding of the APT model. Now, thanks to You, and other researchers from this webpage, I realize that it is not used to predict, but to identify the overpriced/underpriced securities in the diversified portfolio, which is the most important part to mention. As this is my university project, everything here is in educational purposes. After all, I would say, I probably prefer other methods to APT to assess the stock, for example, DCF. Thanks a lot for your help again, Mr Barnard.
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