1. Basing expected returns on the US market is an egregious case of selection bias.
FYI they redo the analysis for the FTSE and the Nikkei and they come to the same conclusion. Also, the theoretical analysis comes out the same even if returns are lower in the future than they have been in the past.
Lower expected return does mean putting a lower share into the risky asset, but expected returns would have to go very low indeed (w/o a corresponding drop in expected volatility) for the analysis not to suggest that those just starting out should use leverage. (2x leverage is way undershooting the target that the math suggests, but they suggest maxing out at 2x leverage for various practical reasons. If expected returns were a bit lower, then 2x would probably still be below the theoretical target for people at the beginning of their careers.)
2. Any mention of the normal distribution...
I am curious about this. It’s my impression that assets tend to become more correlated in a downturn. I’m not sure how much this, or the presence of fat tails, affects things, but their back test on at least three different countries’ data mitigates my concern somewhat.
3. There is a more subtle problem… Books advocating leverage, stocks for the long run, index and forget etc, tend to appear after a run-up in the market
Happily, this was at least not the case here. The book was written in 2008/2009, and published in 2010, just after the financial crisis. And we’re reading this review during the coronavirus pandemic when the S&P is still down 15% from the start of the year.
4. Terrible market returns often coincide with hard times for the portfolio owner, such as unemployment, slumps in the value of other assets and other difficulties.
This is a fair point, which I think was not addressed well enough in the book. But which was addressed well in Jess’s review! (See e.g. his discussion of disability insurance.)
I am curious about this. It’s my impression that assets tend to become more correlated in a downturn. I’m not sure how much this, or the presence of fat tails, affects things, but their back test on at least three different countries’ data mitigates my concern somewhat.
(I don’t know how it applies to this model, but...) price movements are not normally distributed, and any model that assumes they are carries a major risk of blowing up. For example: during the financial crisis Goldman Sachs chief financial officer David Viniar infamously told the Financial Times “we were seeing things that were 25-standard deviation moves, several days in a row.”
What are the chances that a 25-sigma event strikes your investment portfolio?
We should expect a 4σ event to happen twice in our lifetime. A 5σ event occurs about every 5000 years, or once since the beginning of recorded history. A 6σ event might have happened roughly twice in the millions of years since homo sapiens branched off from the other apes. A 7σ event comes along every billion years or so, or four times since our planet coalesced out of a cloud of interstellar dust. We pass the Big Bang somewhere around the 8σ mark. At 20σ, the number of years we’d have to wait is ~10x higher than the number of particles in the universe, etc.
(which is to say, Goldman and friends’ models were disastrously, absurdly, cosmologically wrong.)
AFAIK Benoit Mandelbrot was the first to start warning people about this, and his PhD student Eugene Fama wrote his thesis on it...back in 1965! Which gives you a sense of how crazy it is that people would still try to apply normal distributions to financial markets.
Mandelbrot’s book The Misbehaviour of Markets is worth a read. I’ve also written a summary of his ideas here, in the context of stress-testing the assumptions of the ‘early retirement’ movement.
FYI they redo the analysis for the FTSE and the Nikkei and they come to the same conclusion. Also, the theoretical analysis comes out the same even if returns are lower in the future than they have been in the past.
Lower expected return does mean putting a lower share into the risky asset, but expected returns would have to go very low indeed (w/o a corresponding drop in expected volatility) for the analysis not to suggest that those just starting out should use leverage. (2x leverage is way undershooting the target that the math suggests, but they suggest maxing out at 2x leverage for various practical reasons. If expected returns were a bit lower, then 2x would probably still be below the theoretical target for people at the beginning of their careers.)
I am curious about this. It’s my impression that assets tend to become more correlated in a downturn. I’m not sure how much this, or the presence of fat tails, affects things, but their back test on at least three different countries’ data mitigates my concern somewhat.
Happily, this was at least not the case here. The book was written in 2008/2009, and published in 2010, just after the financial crisis. And we’re reading this review during the coronavirus pandemic when the S&P is still down 15% from the start of the year.
This is a fair point, which I think was not addressed well enough in the book. But which was addressed well in Jess’s review! (See e.g. his discussion of disability insurance.)
(I don’t know how it applies to this model, but...) price movements are not normally distributed, and any model that assumes they are carries a major risk of blowing up. For example: during the financial crisis Goldman Sachs chief financial officer David Viniar infamously told the Financial Times “we were seeing things that were 25-standard deviation moves, several days in a row.”
What are the chances that a 25-sigma event strikes your investment portfolio?
We should expect a 4σ event to happen twice in our lifetime. A 5σ event occurs about every 5000 years, or once since the beginning of recorded history. A 6σ event might have happened roughly twice in the millions of years since homo sapiens branched off from the other apes. A 7σ event comes along every billion years or so, or four times since our planet coalesced out of a cloud of interstellar dust. We pass the Big Bang somewhere around the 8σ mark. At 20σ, the number of years we’d have to wait is ~10x higher than the number of particles in the universe, etc.
(which is to say, Goldman and friends’ models were disastrously, absurdly, cosmologically wrong.)
AFAIK Benoit Mandelbrot was the first to start warning people about this, and his PhD student Eugene Fama wrote his thesis on it...back in 1965! Which gives you a sense of how crazy it is that people would still try to apply normal distributions to financial markets.
Mandelbrot’s book The Misbehaviour of Markets is worth a read. I’ve also written a summary of his ideas here, in the context of stress-testing the assumptions of the ‘early retirement’ movement.