Maybe I didn’t make it clear, but difference between investor returns and investment returns is a non-issue, because such models are about instantaneous/incremental returns, not total returns. The simplest way to think about it is to split up time into segments. At the start of each segment you construct your portfolio (which could include cash) and it stays constant over that segment. At the end of the segment you observe the return to your portfolio over that period. The geometric sum of these returns is going to be your total return. Both CAPM and Falkestein’s model are about these period returns, not total returns. They are also only about the change in value beginning to end; the Var() does not describe the back and forth motion during the period, it describes your uncertainty at the beginning of the period about what the end of the period is going to look like.
I think maybe I understand what you were saying in the beginning. I’ll explain that and why I think it’s wrong, and you tell me if I’ve misunderstood something. I’m taking your first post to indicate your core point; if it’s changed, tell me.
OK, so I think what your idea is that your idea was that beta is like the variance of a portfolio price around a path. You can profit from this by buying when it’s below the path since this implies the price will at some point be above the path, giving you a profit.
The problem with is that financial markets are pretty efficient. This means that prices are a random walk, meaning the expected incremental return on an asset is independent of past returns. The price of an asset being below trend does not imply that above average expected incremental returns. You can think of this as saying that any changes in a portfolio price are permanent; if a stock price goes down, on average, it’s going to stay down; it might go up, but it’s just as likely to go down further.
1) I care about the investor return, not the asset return or any of the other metrics you listed, because that’s the return I get.
2) I wasn’t suggesting that an investor could buy on the lows. I was saying that the investor could buy in every period, but only an amount that is constant in dollar terms (or in terms of some other risk-free asset). This would then exceed the asset’s average return, though both might be negative.
1) Obviously you’re concered about invstor return (well utility anyway), I never intended to suggested there was any other metric you’d be interested in. Surely our previous conversations should have convinced you I’m not one to make that kind of mistake frequently.
2) Dollar cost averaging gets you something if there’s mean reversion. Otherwise it gains you nothing (might not cost you anything either) for the simple reason that asset prices are random walks. This is a standard result (http://www.moneychimp.com/features/dollar_cost.htm). If you think Falkenstein’s model implies that dollar cost averaging is a superior strategy, then I think you’ve misunderstood something. I’m not sure what it is though, I tried to reexplain the concepts which I thought you might be misunderstanding. Could you reexplain why you think it would get you superior performance using the kind of multi period model I was talking about?
Okay, I hadn’t actually experimented with the math on that so I can’t defend DCA as amplifying returns under volatility. So I don’t have much more to say in objection to the result you’ve posted either.
1) I’m not sure what different metrics you though I suggested. To clarify, CAPM and Falkenstein’s model are about returns for a constant portfolio over a given period. If you want to talk about a changing portfolio, you’ll have to approximate this as several time periods each with a different constant portolio and geomtrically average the returns.
Given as it doesn’t address any of the issues I raised (like the difference between investor returns and investment returns), no.
Maybe I didn’t make it clear, but difference between investor returns and investment returns is a non-issue, because such models are about instantaneous/incremental returns, not total returns. The simplest way to think about it is to split up time into segments. At the start of each segment you construct your portfolio (which could include cash) and it stays constant over that segment. At the end of the segment you observe the return to your portfolio over that period. The geometric sum of these returns is going to be your total return. Both CAPM and Falkestein’s model are about these period returns, not total returns. They are also only about the change in value beginning to end; the Var() does not describe the back and forth motion during the period, it describes your uncertainty at the beginning of the period about what the end of the period is going to look like.
I think maybe I understand what you were saying in the beginning. I’ll explain that and why I think it’s wrong, and you tell me if I’ve misunderstood something. I’m taking your first post to indicate your core point; if it’s changed, tell me.
OK, so I think what your idea is that your idea was that beta is like the variance of a portfolio price around a path. You can profit from this by buying when it’s below the path since this implies the price will at some point be above the path, giving you a profit.
The problem with is that financial markets are pretty efficient. This means that prices are a random walk, meaning the expected incremental return on an asset is independent of past returns. The price of an asset being below trend does not imply that above average expected incremental returns. You can think of this as saying that any changes in a portfolio price are permanent; if a stock price goes down, on average, it’s going to stay down; it might go up, but it’s just as likely to go down further.
1) I care about the investor return, not the asset return or any of the other metrics you listed, because that’s the return I get.
2) I wasn’t suggesting that an investor could buy on the lows. I was saying that the investor could buy in every period, but only an amount that is constant in dollar terms (or in terms of some other risk-free asset). This would then exceed the asset’s average return, though both might be negative.
1) Obviously you’re concered about invstor return (well utility anyway), I never intended to suggested there was any other metric you’d be interested in. Surely our previous conversations should have convinced you I’m not one to make that kind of mistake frequently.
2) Dollar cost averaging gets you something if there’s mean reversion. Otherwise it gains you nothing (might not cost you anything either) for the simple reason that asset prices are random walks. This is a standard result (http://www.moneychimp.com/features/dollar_cost.htm). If you think Falkenstein’s model implies that dollar cost averaging is a superior strategy, then I think you’ve misunderstood something. I’m not sure what it is though, I tried to reexplain the concepts which I thought you might be misunderstanding. Could you reexplain why you think it would get you superior performance using the kind of multi period model I was talking about?
Okay, I hadn’t actually experimented with the math on that so I can’t defend DCA as amplifying returns under volatility. So I don’t have much more to say in objection to the result you’ve posted either.
1) I’m not sure what different metrics you though I suggested. To clarify, CAPM and Falkenstein’s model are about returns for a constant portfolio over a given period. If you want to talk about a changing portfolio, you’ll have to approximate this as several time periods each with a different constant portolio and geomtrically average the returns.