How does the average person have leverage of > 1 as this means shorting LT treasuries? How can you avoid transaction costs AND rebalance [what exactly] annually.
This all seems as nonsensical as technical trading on prices ASSUMING NO TRANSACTION COSTS.
L=1 means 100% equities. Where is the 1987 stock market drop? Not visible. How can that be?
The analysis should assume any starting point and evaluate the 10 year returns. How many years do you get real value losses? [Wasn't this the case 1970-1980 - that is visible in teh charts?]
The story seems to be that stocks outperform bonds, but leverage doesn't work well in the long term. This seems to be because you may be forced to sell during a downturn to cover one's borrowing, If you aren't leveraged, you can sit out a downturn. If you have loans to cover, there go your higher returns. Leverage can be a good short term tool, but it has a serious downside in the long run.
One important thing to consider is that if you started investing at age twenty in 1870, you have probably been dead for over seventy years now. Of course, if you are a corporation or a family trust, that doesn't matter which is a good argument for high taxes on corporations and trusts.
One more thing. Peters' critics often screw up by affirming the consequent. Peters is not saying that there is no such thing as utility or risk aversion; he is saying that in cases where one is running a self-financing portfolio with reinvestment, it is not *necessary* to evoke risk aversion to explain why investors prefer higher time average returns because that is the rational choice.
Here is why that is relevant to the optimal leverage ratio. These thought experiments - parameterizing a functional form from historical data like Peters or assuming the historical distribution is the true distribution like RA Yekwang Hwang - assume that you know the betting odds and payoffs with certainty; but of course you do not. However, the effects of getting the optimal leverage ratio wrong are asymmetric with respect to risk. If you overestimate L, you decrease returns and *increase* risk. If you underestimate L, you decrease returns but *decrease* risk; a too-low leverage ratio has a higher risk-adjusted return than a too-high leverage ratio.
So as you can see, thinking in ergodic terms is perfectly consistent with accounting for risk-aversion.
BTW, I personally think Peters' earlier (2009) paper, Optimal leverage from Non-Ergodicity, gives a more thorough account of optimal leverage than the Peters & Adamou paper.
Is "RA Yekwang Hwang" *your RA*? If so, very cool, and congratulations!
I think you ought to distinguish between the normative claim made by Peters & Adamou - that an efficient market should cause optimal leverage to be 1 - and the positive empirical claim, which was as follows:
"based on price data only, but pretending that there are no costs to trading and borrowing, optimal leverage is greater than one ... However, once our approximations of trading costs are included, real optimal leverage is seen to be very close or even equal to one."
Both claims seem consistent with that made by RA Yekwang Hwang?
I would add that if you only test for "bankruptcy" annually, at the same frequency you rebalance, then you are certain to overestimate the optimal L. Unfortunately, it is hard to test for "bankruptcy" when L > 1 because that happens not when your portfolio value falls to zero but when you fail to meet a margin call - a more stringent requirement. But I shouldn't think that the necessary historical data is available to make this test.
I'll need to read through a couple of the papers you linked to but retrospective analyses such as these are pretty much useless. "Whatever can go wrong, will go wrong" and as Ales Tolley notes there are some poor assumptions. The number of sophisticate hedge funds that have a proven track record is on the very small side and were one investing say in 1970, putting a significant portion of cash into Berkshire-Hathaway would make one set for financial well being (I was a little late to that party investing in 1995).
Past performance in the stock market is no guarantee of future performance. PE ratios are much higher now than the historical average. Also the stock market has never had to deal with climate change before. On the other hand, history has shown it is foolish to bet against American corporations. They will do whatever it takes to drive their stock price up. So basically the stock market is always balanced 50/50 between buyers and sellers.
Agree. Also, in the early 20th century stocks had very low PE ratios and were considered very risky. Now, as you say, they have far higher ratios.
IIRC from my finance history, ST treasuries offer no +ve inflation adjusted returns and LT treasuries around 2%./pa. Using the chart data for L=0, with 152 years, I show a 2.26% annual return for LT treasuries, which is about the 2% mentioned above. But after transaction costs? Until 1976 in the US and 1986 in the UK, commission rates (transaction costs) where high. That would have shaved off the returns, and that in addition to the Bid/Ask spreads every time a transaction is done.
IMO, these charts are snake-oil. [not so dissimilar to the VC crypto - and web3- bros.]
"start in January 1871 with an initial wealth W,
choose a leverage L,
invest W*L in the stock market,
invest W*(1-L) in safe long-term Treasury bonds,
reinvest interest and dividends,
pay no taxes,
incur no transactions costs,
and rebalance every January.
"
How does the average person have leverage of > 1 as this means shorting LT treasuries? How can you avoid transaction costs AND rebalance [what exactly] annually.
This all seems as nonsensical as technical trading on prices ASSUMING NO TRANSACTION COSTS.
L=1 means 100% equities. Where is the 1987 stock market drop? Not visible. How can that be?
The analysis should assume any starting point and evaluate the 10 year returns. How many years do you get real value losses? [Wasn't this the case 1970-1980 - that is visible in teh charts?]
Math typo? What does W*(1-L) mean when L>1, as is the case for optimal L = 1.6?
The story seems to be that stocks outperform bonds, but leverage doesn't work well in the long term. This seems to be because you may be forced to sell during a downturn to cover one's borrowing, If you aren't leveraged, you can sit out a downturn. If you have loans to cover, there go your higher returns. Leverage can be a good short term tool, but it has a serious downside in the long run.
One important thing to consider is that if you started investing at age twenty in 1870, you have probably been dead for over seventy years now. Of course, if you are a corporation or a family trust, that doesn't matter which is a good argument for high taxes on corporations and trusts.
Indeed. You go bankrupt just when your expected future returns are brightest...
One more thing. Peters' critics often screw up by affirming the consequent. Peters is not saying that there is no such thing as utility or risk aversion; he is saying that in cases where one is running a self-financing portfolio with reinvestment, it is not *necessary* to evoke risk aversion to explain why investors prefer higher time average returns because that is the rational choice.
Here is why that is relevant to the optimal leverage ratio. These thought experiments - parameterizing a functional form from historical data like Peters or assuming the historical distribution is the true distribution like RA Yekwang Hwang - assume that you know the betting odds and payoffs with certainty; but of course you do not. However, the effects of getting the optimal leverage ratio wrong are asymmetric with respect to risk. If you overestimate L, you decrease returns and *increase* risk. If you underestimate L, you decrease returns but *decrease* risk; a too-low leverage ratio has a higher risk-adjusted return than a too-high leverage ratio.
So as you can see, thinking in ergodic terms is perfectly consistent with accounting for risk-aversion.
BTW, I personally think Peters' earlier (2009) paper, Optimal leverage from Non-Ergodicity, gives a more thorough account of optimal leverage than the Peters & Adamou paper.
Is "RA Yekwang Hwang" *your RA*? If so, very cool, and congratulations!
I think you ought to distinguish between the normative claim made by Peters & Adamou - that an efficient market should cause optimal leverage to be 1 - and the positive empirical claim, which was as follows:
"based on price data only, but pretending that there are no costs to trading and borrowing, optimal leverage is greater than one ... However, once our approximations of trading costs are included, real optimal leverage is seen to be very close or even equal to one."
Both claims seem consistent with that made by RA Yekwang Hwang?
I would add that if you only test for "bankruptcy" annually, at the same frequency you rebalance, then you are certain to overestimate the optimal L. Unfortunately, it is hard to test for "bankruptcy" when L > 1 because that happens not when your portfolio value falls to zero but when you fail to meet a margin call - a more stringent requirement. But I shouldn't think that the necessary historical data is available to make this test.
I forgot to note that Peters & Adamou rebalance / test bankruptcy daily, not annually.
I'll need to read through a couple of the papers you linked to but retrospective analyses such as these are pretty much useless. "Whatever can go wrong, will go wrong" and as Ales Tolley notes there are some poor assumptions. The number of sophisticate hedge funds that have a proven track record is on the very small side and were one investing say in 1970, putting a significant portion of cash into Berkshire-Hathaway would make one set for financial well being (I was a little late to that party investing in 1995).
Past performance in the stock market is no guarantee of future performance. PE ratios are much higher now than the historical average. Also the stock market has never had to deal with climate change before. On the other hand, history has shown it is foolish to bet against American corporations. They will do whatever it takes to drive their stock price up. So basically the stock market is always balanced 50/50 between buyers and sellers.
Agree. Also, in the early 20th century stocks had very low PE ratios and were considered very risky. Now, as you say, they have far higher ratios.
IIRC from my finance history, ST treasuries offer no +ve inflation adjusted returns and LT treasuries around 2%./pa. Using the chart data for L=0, with 152 years, I show a 2.26% annual return for LT treasuries, which is about the 2% mentioned above. But after transaction costs? Until 1976 in the US and 1986 in the UK, commission rates (transaction costs) where high. That would have shaved off the returns, and that in addition to the Bid/Ask spreads every time a transaction is done.
IMO, these charts are snake-oil. [not so dissimilar to the VC crypto - and web3- bros.]