I think using actual values and therefore calculating betas and so on would just lengthen the lecture tremendously. By understanding the principles you should be able to calculate these yourself.
Hi, That was really helpful but I have a quick question: In step 4 when you were trying to calculate Alpha by subtracting the expected return from the actual mean return. But isn' the actual mean return RI is the one you used to find out Lambdas in step 3 the cross sectional regression? Should' these two be the same?
Hi Michael, I looked at the calculations and they look fine. Perhaps it might help you better understand if you ask me why the two should not be the same or even better, what possible issues do you see in analytical estimates if the two are same. Want to give it a shot?
Gammas are regression estimates once you regress betas on average returns. Essentially, gammas help estimate the best linear relationship between factor sensitivities and past average returns of N firms.
Hi, thanks for the video. It was relatively easy to understand. May I ask how did the risk free rate at the end of step 3 (cross sectional analysis) come about? From my understanding, you ran a regression with mean returns ri as the y variable and betas as the x variables to construct the APT equation. I believe there would be an intercept, but would it the risk free rate?
Chua Khiong Jian The easiest way to think about this would be to go back to CAPM. Its a one factor model where expected return is equal to risk free rate plus risk premium. Think about extending that model by including more factors. Risk free rate would remain right?
Hi, for Step 4 and 5, wouldn't it be the opposite? So if alpha is more than 0, that would mean that the stock went up in price more than we predicted, so it's likely overpriced and we should go short. Or am I missing something? Also, thanks for the video.
Ok, I know what I was missing. In step 4, when you say "actual" (mean) returns, I was thinking you meant future (i.e., live) returns. But you when you say actual, you mean it as "actual historic" mean returns. Therefore, when the alpha of an asset is greater than 0, we're saying that, historically, this particular asset has had better returns as compared to the other assets in the portfolio, specifically regarding this asset's returns with respect to the chosen macro-level market factors.
hello, the elements in this video like, alpha, beta, factors and etc. are quite advance for me to understand as i am a beginner. can you please recommend me what should i watch or read to understand the technicalities behind this knowledge? Please reply. Thanks!
Hi Waleed, Alpha, beta etc are just symbols. You can replace them with symbols you like. But you can't understand arbitrage pricing theory without "factors". Start with learning what stocks, bonds, ETFs, mutual funds are, how they work and how they're different from each other. Then you can go to options. This tutorial is designed for students of financial theory.
HI, thanks very much for your reply, may i ask like with what symbols can i replace them, and whats the most fundamental reason behind it, (like why do we do it?)
Hi Waleed, Send me a message with your questions, finance background and motivation for learning financial theory. I might be better able to help you that way. There are a number of tests of APT and multiple reasons to employ it. In this particular tutorial, we show how APT can be implemented to construct a long/short portfolio to generate potential alpha.
Very good video, just one question. In step 3, the cross sectional regression, the gammas estimated are the risk premiums for the factors, is that correct, and to find the risk premium we collect all the returns of all assets and regress on all previously found factor loadings for each factor?
Thank for the question and the comment! I think it would be clearer to mention the jargon, risk premium, in the lecture for viewers who have partial knowledge from different lectures.
Thanks for the suggestion. While I try to do that in most videos, I assumed here that an average viewer of this particular tutorial has prior understanding of finance. I will take your suggestion in consideration going forward.
Hi thank you for this video! In which way are the Lambdas and Gammas different? Or are they basically the same - meaning Lambda being the theoretical term and gamma the actual estiamte?
They are reflecting different parameter values. I would look at them as two separate parameters. Estimated values are typically not reflected with a different sign. Statisticians typically just put a ^ on the same parameter once estimated.
@@fincampuslecturehall4833 Thank you for the quick response! But both lambda and gamma represent the risk premia associated with the specific factors right? How are they different?
@@simonbrinkmann1333 Lambdas are risk premia associated with certain factors. Perhaps you can suggest what gammas actually represent and how they're different from lambdas. If you don't get it right, I'll try to explain. Hint: What is a cross-sectional regression?
finCampus Lecture Hall maybe it‘s the following: lambda could represent the stylized risk premium chosen by the researcher to extract the beta loading in a time series regression using the past return data of an asset. In the third step the actual risk premia must be predicted rather than using a theoretical construction. Thus the betas and returns from all assets of step 2 might be used in a cross section to extract gammas which may represent the average risk premia. Thus the core difference would be that lambda is a constructed risk premium, while gamma is the actual estimated risk premium. Please correct me when I‘m wrong.
Hi. This video made so much staff clearer, thanks for that. However, I have couple of questions regarding the APT in this video. 1) In step 2 (5:00), should we find the risk premiums for each macro factors before regressing time series regression, or we just regress macro factors as given (like GDP return - risk free rate, or just GDP return) to find betas of each company return? 2) In step 3 (9:00), how did you include the risk free rate for each cross sectional regression? Does it mean that we subtract the risk free rate from the each beta obtained from step 2 and then regress, and thus obtain it in the form of intercept? Because, actually, program gives only intercept and estimates(betas)? Or you just regressed on betas obtained from step 2 and included risk free rate by hand? I am a bit confused here. Thanks a lot.
1) Have you tried both? If so, how do the results differ in terms of causality? 2) I am just trying to calculate risk premium over risk free rate. You can choose a different number that you feel is suited to your model (especially now that risk free rate in the US is so low). But we never subtract risk free rate from each beta. Beta is a regression coefficient, not a variable that defines risk premium.
1) yes, I have run both regression. I got the same models, so that subtracting risk-free rates from the factors seems to make no change in the estimates, their t-score, se, and p-values. 2) I got it, Initially I was a bit confused why did you mark the intercept of the cross sectional regression as a risk-free rate, like what is the economic interpretation of the beta. Thanks a lot.
Thank you, it was pretty good. I want to do an investigation about estimating this APT model into the Perú's Alternative Stock Market, so it works for bonds too?
What's an Alternative Stock Market? Are you referring to bond market? Best way to know whether it works for the universe of bonds you're considering is by actually trying it. Bonds have other dynamics (duration being one) that stocks don't and mean reversion process is different from equities so you'll have to select factors accordingly and think carefully about how you set up the model.
finCampus Lecture Hall Right, thanks again. The Perú's Alternative Stock Market is essentially a bond market for small business. May you recomend me any other good reference (works, books) to do it, please?
Eduardo Emilio Haro Pimentel Since you mentioned bond market for small businesses, you might want to look at how distressed credit funds evaluate companies. It's usually a bottom up analysis where focus is on estimating enterprise value. Start with google.
Beta here is just a regression beta. It does not represent price of the asset. You might want to look up some introductory videos on youtube on linear regression or consult a basic textbook on the subject.
+Vaibhav D I think you need to optimize a portfolio and impose an excess return constraint of 5%. I'm not sure how your question is related to APT - perhaps only enter a trade if alpha exceeds 5%?
+finCampus Lecture Hall : Thanks for the reply. yes, I have a project, where I need to form a alpha portfolio by the returns that are generated from the APT model and then Backtest it with the original returns. I have one simple question for you: I am getting only one variable that is significant. So, in that case, when I calculate the Expected returns of the security, do I include all the factors or only that one factor + rf?
How does he find the formula for alpha? He says if Alpha is greater than 0, then stock is undervalued. I get it. But what justifies you that is the alpha? Alpha in simple regression is ybar - b*xbar. You wrote Actual - Predicted. How ???? It would have been better if you explained these concepts than going straight into the equation.
Allow me to ask you a question: what's the difference between ybar - b*xbar and Actual - Predicted? If you watch second half of the video again, I do explain the two concepts. That said, I appreciate your feedback and will take it into consideration in future.
If you look at Step 3, from 9:00 onwards, I am not using the relation that you mention. Instead of average return, you can take median return and back out alpha that way. This is not risk-free arbitrage. Your alpha depends on your choice of "y-variable" and that choice can be subjective.
OK.😊
Amazing!🎉😊😊
Great work! Got it fully!
It would be nice if you actually explained this with numbers and real stocks rather than a bunch of variables
I think using actual values and therefore calculating betas and so on would just lengthen the lecture tremendously. By understanding the principles you should be able to calculate these yourself.
you can pretty much replicate the process using excel
Hi,
That was really helpful but I have a quick question:
In step 4 when you were trying to calculate Alpha by subtracting the expected return from the actual mean return. But isn' the actual mean return RI is the one you used to find out Lambdas in step 3 the cross sectional regression? Should' these two be the same?
Hi Michael, I looked at the calculations and they look fine. Perhaps it might help you better understand if you ask me why the two should not be the same or even better, what possible issues do you see in analytical estimates if the two are same. Want to give it a shot?
Thanks! I didn't quite understand how you obtained the gamma values, or what they represent.
Gammas are regression estimates once you regress betas on average returns. Essentially, gammas help estimate the best linear relationship between factor sensitivities and past average returns of N firms.
Hi, thanks for the video. It was relatively easy to understand. May I ask how did the risk free rate at the end of step 3 (cross sectional analysis) come about? From my understanding, you ran a regression with mean returns ri as the y variable and betas as the x variables to construct the APT equation. I believe there would be an intercept, but would it the risk free rate?
Chua Khiong Jian The easiest way to think about this would be to go back to CAPM. Its a one factor model where expected return is equal to risk free rate plus risk premium. Think about extending that model by including more factors. Risk free rate would remain right?
finCampus Lecture Hall Hi Thanks. I will try figuring it out, I think i have some problems with the whole concept of multifactor APT.
Hi, for Step 4 and 5, wouldn't it be the opposite? So if alpha is more than 0, that would mean that the stock went up in price more than we predicted, so it's likely overpriced and we should go short. Or am I missing something?
Also, thanks for the video.
Ok, I know what I was missing. In step 4, when you say "actual" (mean) returns, I was thinking you meant future (i.e., live) returns. But you when you say actual, you mean it as "actual historic" mean returns. Therefore, when the alpha of an asset is greater than 0, we're saying that, historically, this particular asset has had better returns as compared to the other assets in the portfolio, specifically regarding this asset's returns with respect to the chosen macro-level market factors.
hello
why do you use cross sectional regressions?
great video, it helped me get the intuition behind it
hello, the elements in this video like, alpha, beta, factors and etc. are quite advance for me to understand as i am a beginner. can you please recommend me what should i watch or read to understand the technicalities behind this knowledge?
Please reply. Thanks!
Hi Waleed,
Alpha, beta etc are just symbols. You can replace them with symbols you like. But you can't understand arbitrage pricing theory without "factors". Start with learning what stocks, bonds, ETFs, mutual funds are, how they work and how they're different from each other. Then you can go to options. This tutorial is designed for students of financial theory.
HI,
thanks very much for your reply, may i ask like with what symbols can i replace them, and whats the most fundamental reason behind it, (like why do we do it?)
Hi Waleed,
Send me a message with your questions, finance background and motivation for learning financial theory. I might be better able to help you that way. There are a number of tests of APT and multiple reasons to employ it. In this particular tutorial, we show how APT can be implemented to construct a long/short portfolio to generate potential alpha.
What if you have multicollinearity between the macro risk factors? How to select to most significant factors?
Perhaps you can use lasso or select only the variable that you think is more important.
Very good video, just one question. In step 3, the cross sectional regression, the gammas estimated are the risk premiums for the factors, is that correct, and to find the risk premium we collect all the returns of all assets and regress on all previously found factor loadings for each factor?
Your understanding is correct.
Thank for the question and the comment! I think it would be clearer to mention the jargon, risk premium, in the lecture for viewers who have partial knowledge from different lectures.
Thanks for the suggestion. While I try to do that in most videos, I assumed here that an average viewer of this particular tutorial has prior understanding of finance. I will take your suggestion in consideration going forward.
Hi thank you for this video! In which way are the Lambdas and Gammas different? Or are they basically the same - meaning Lambda being the theoretical term and gamma the actual estiamte?
They are reflecting different parameter values. I would look at them as two separate parameters. Estimated values are typically not reflected with a different sign. Statisticians typically just put a ^ on the same parameter once estimated.
@@fincampuslecturehall4833 Thank you for the quick response! But both lambda and gamma represent the risk premia associated with the specific factors right? How are they different?
@@simonbrinkmann1333 Lambdas are risk premia associated with certain factors. Perhaps you can suggest what gammas actually represent and how they're different from lambdas. If you don't get it right, I'll try to explain. Hint: What is a cross-sectional regression?
finCampus Lecture Hall maybe it‘s the following: lambda could represent the stylized risk premium chosen by the researcher to extract the beta loading in a time series regression using the past return data of an asset. In the third step the actual risk premia must be predicted rather than using a theoretical construction. Thus the betas and returns from all assets of step 2 might be used in a cross section to extract gammas which may represent the average risk premia. Thus the core difference would be that lambda is a constructed risk premium, while gamma is the actual estimated risk premium. Please correct me when I‘m wrong.
@@TheJoker9555 Good job!
Hi. This video made so much staff clearer, thanks for that. However, I have couple of questions regarding the APT in this video. 1) In step 2 (5:00), should we find the risk premiums for each macro factors before regressing time series regression, or we just regress macro factors as given (like GDP return - risk free rate, or just GDP return) to find betas of each company return?
2) In step 3 (9:00), how did you include the risk free rate for each cross sectional regression? Does it mean that we subtract the risk free rate from the each beta obtained from step 2 and then regress, and thus obtain it in the form of intercept? Because, actually, program gives only intercept and estimates(betas)? Or you just regressed on betas obtained from step 2 and included risk free rate by hand? I am a bit confused here.
Thanks a lot.
1) Have you tried both? If so, how do the results differ in terms of causality?
2) I am just trying to calculate risk premium over risk free rate. You can choose a different number that you feel is suited to your model (especially now that risk free rate in the US is so low). But we never subtract risk free rate from each beta. Beta is a regression coefficient, not a variable that defines risk premium.
1) yes, I have run both regression. I got the same models, so that subtracting risk-free rates from the factors seems to make no change in the estimates, their t-score, se, and p-values.
2) I got it, Initially I was a bit confused why did you mark the intercept of the cross sectional regression as a risk-free rate, like what is the economic interpretation of the beta.
Thanks a lot.
Great. For 1) can you provide a causal interpretation?
Thank you, it was pretty good. I want to do an investigation about estimating this APT model into the Perú's Alternative Stock Market, so it works for bonds too?
What's an Alternative Stock Market? Are you referring to bond market? Best way to know whether it works for the universe of bonds you're considering is by actually trying it. Bonds have other dynamics (duration being one) that stocks don't and mean reversion process is different from equities so you'll have to select factors accordingly and think carefully about how you set up the model.
finCampus Lecture Hall Right, thanks again. The Perú's Alternative Stock Market is essentially a bond market for small business. May you recomend me any other good reference (works, books) to do it, please?
Eduardo Emilio Haro Pimentel Since you mentioned bond market for small businesses, you might want to look at how distressed credit funds evaluate companies. It's usually a bottom up analysis where focus is on estimating enterprise value. Start with google.
finCampus Lecture Hall Thank you, i've decided to work with the 15 biggest equities. this explanation is the two step test of Fama y MacBeth, right?
Eduardo Emilio Haro Pimentel Hi, Can you please rephrase the question?
excellent thanks
hello, I want to ask about the beta in second step what does it represent ? is it the price of the asset?
Beta here is just a regression beta. It does not represent price of the asset. You might want to look up some introductory videos on youtube on linear regression or consult a basic textbook on the subject.
very nice video. Thanks a lot. I have a question : how can I construct a portfolio with a constraint in alpha? like a portfolio with an alpha of 5%.
+Vaibhav D I think you need to optimize a portfolio and impose an excess return constraint of 5%. I'm not sure how your question is related to APT - perhaps only enter a trade if alpha exceeds 5%?
+finCampus Lecture Hall : Thanks for the reply. yes, I have a project, where I need to form a alpha portfolio by the returns that are generated from the APT model and then Backtest it with the original returns.
I have one simple question for you: I am getting only one variable that is significant. So, in that case, when I calculate the Expected returns of the security, do I include all the factors or only that one factor + rf?
good
didn't you mean "fitted value" when you say 'predicted value" expressed as the sum of those terms??
How does he find the formula for alpha? He says if Alpha is greater than 0, then stock is undervalued. I get it. But what justifies you that is the alpha? Alpha in simple regression is ybar - b*xbar. You wrote Actual - Predicted. How ???? It would have been better if you explained these concepts than going straight into the equation.
Allow me to ask you a question: what's the difference between ybar - b*xbar and Actual - Predicted? If you watch second half of the video again, I do explain the two concepts. That said, I appreciate your feedback and will take it into consideration in future.
Oh okay. Thanks. I get your concept. But X bar is the average of x right? Is it exactly the predicted value?
I went through the video again. I did not see any X bar. Can you please elaborate?
For simple regression there is a formula for beta and alpha. Alpha is defined as ybar - b*xbar . Did you use the same concept here?
If you look at Step 3, from 9:00 onwards, I am not using the relation that you mention. Instead of average return, you can take median return and back out alpha that way. This is not risk-free arbitrage. Your alpha depends on your choice of "y-variable" and that choice can be subjective.