On the one hand, if the stock market is "Efficient", then one should not be able
to predict how much the stock will go up or down from its current price based on
information other than the stock price. The Efficient Market Hypothesis (EMH)
teaches us that all the information about a company is available and priced into
its current stock price. If we
could predict from other information that
the stock would rise, then that would cause the
current price of the
stock to rise in anticipation of this.
On the other hand, if we find we can predict outsize or undersize growth in
stock price based on non-price information, then the EMH is by no means
completely true, and we may be able to increase our earnings by trading shares,
or options on those shares, rather than just buying them and holding them.
Here, we consider Berkshire Hathaway stock. We will work with the "B" shares for
convenience. In particular, we will look at the "Price/Book" ratio of the stock
to see if there is information in this metric that can help us make outsize
returns from trading BRK.B stock, or options on this stock.
In this figure, we show the stock price and the book value of a BRK.B share over
the last 5 years. The blue line shows the stock price in dollars over those 5
years, it has risen from about $200/share to about $450/share during that time.
The green line shows the "Book value per share" for the company. The Book value
of a company is an estimate of the value of the company calculated in a very
highly specified way. For this green line, the amount of Book value associated
with each BRK.B share is calculated and shown. The Book value is calculated 4
times a year and reported by the company, we see the Book value rising and
falling ever 3 months in the figure. Finally, the red line is "Price/Book", the
ratio of the stock price to the stock's book value. Note the Price/Book has
values shown on the right-hand y-axis, ranging from 1.0 to about 1.7 over these
5 years.
We hypothesize that Book/Share is a reasonable measure of the true, or intrinsic
value of a share of stock. Then when the P/B is high, the price of a share is
high, for example at P/B=1.6, someone buying a share of BRK.B is paying a 60%
premium over its Book value to buy that share. On the other hand, when the
P/B=1.2, someone buying the share at that point is paying only a 20% premium
above book to buy a share.
Looking at the time-variation of P/B, we see it varying in a possibly random way
between about 1.0 and 1.7. If this is true, we would expect the stock to be a
better buy when P/B is lower, and $1 of Book value is selling at a low premium,
then when P/B is higher. Perhaps we will make more money if we buy the stock
when P/B is lower than when it is higher?
In this figure, we show how much money you would expect to make over a two-year
holding period when you buy a share of BRK.B at a particular P/B ratio. The
x-axis shows the P/B ratio at which the BRK.B share is purchased. The blue line
shows the ratio of the stock price 2 years after the share is purchased to the
stock price when the share was purchased. So for example, from this chart we
look at 1.2 on the x-axis, representing times when we could purchase a share at
a price = 1.2*Book/Share. Looking at the curve, we see it's y-axis value at P/B
= 1.2 is price=1.5. Here, price represents c_stock/o_stock, the ratio of the
c_stock, the stock price at "close," 2 years after purchase, to o_stock, the
stock price at open, when we bought the share. That this ratio is 1.5 on this
plot means that averaged over many time-periods where the stock could have been
bought at P/B = 1.2, the average stock price the stock could be sold at after 2
years is 1.5*o_stock, a 50% gain in two years of holding the stock.
Looking over the whole range of P/B plotted, we see that the expected earnings
from holding a share for 2 years varies tremendously depending on the P/B of the
stock when it is purchased. For P/B ~= 1.1, we expect a 70% return on our
investment in 2 years, or at least that has been our return for such purchases
averaged over the last 5 years of stock prices. At the other end of the plot, of
P/B = 1.6 we would, on average, have made only about 15% profit in 2 years.
By the way, looking at the label on the title of the plot, it is
BRK-B_STOCK_ddays_504. "ddays_504" means we do the average return calculation
assuming the stock is held for 504 trading days. There are about 252 trading
days per year that the stock market is open, so "ddays_504" is what we do to
find the two year return of the stock.
In this figure, we look at how much money you would expect to make over only a
one-year holding period. The curve is very similarly shaped to the
two-year curve previously shown. Indeed, it looks like the 1-year curve is
just 20% lower than the 2-year curve. That is, the 2-year curve went from
70% return down to 20% return as P/B went from 1.1 up to 1.6, while the 1-year
curve goes from 50% return to about 0% return over that same P/B. One
might even hypothesize that after 1 year of growth, the stock "forgets" what P/B
you originally purchased it at, and just earns you, on average, another 20% for
the next year that you hold it.
We now look at the returns after just 6 months. We still see a higher return
when buying at low P/B, but the return at P/B=1.1 is 25% over 6 months vs 50%
over 1 year. But we now see an interesting phenomenon when buying at higher
P/B. At P/B ~= 1.3, the average return on holding the shares for 6 months
is negative! One would expect to lose 5% of value on these investments, or
at least on average that is what has happened during the last 5 years.
This suggests that it is possible to have the stock on sale for such a high
price, that not too long after buying the stock at this price the stock price is
actually lower.
Going down to only a 3-month holding period of the purchased stock, we see the
predictive value on return of the various P/B stock prices we might buy at is
becoming degraded, noisier in some sense. We still see evidence of a
better return for P/B < 1.3. But above 1.3 we sort of see a mish-mosh
of returns ranging from a gain of 5% to a loss of 2.5%.
Finally, we complete the picture showing the investment returns over 21 trading
days, about 1 month of holding time for the purchased shares. For the
truly inexpensive purchase prices P/B <= 1.2, we see a pretty strong
prediction of 8% returns on average, and 8% in 1 month is pretty
spectacular. But for P/B > 1.2 or so, we see a mish-mosh of 1 month
returns ranging from +4% down to -2%.
CONCLUSION
In summary, we see strong evidence that the price at which we buy stock provides quite a lot of information about how well this investment will perform over the next 6 months to 1 year. For time-scales shorter than 6 months, the results are not as clear, although for very low P/B ratios (very cheap stock prices) we still predict outperformance.
