Investment Strategies
Here are some investment strategies for your consideration. We examine how
each strategy would have performed over the past seven-plus years. Three-month
Treasury bill rates (secondary market, discount basis) are used for the base
fund. Short-term bond ETFs don't go back far enough.
Each strategy (except SONGW) operates pretty much the same way (most of the
time). You invest in an ex post Sharpe-optimal portfolio, SOLNG, SOLNU,
.... Each week, on the first business day of the week, you check your
investment to see how its doing (Portfolio Calculator). If its Sharpe Ratio is
not too far from the optimal Sharpe Ratio, you let things ride. Otherwise you
reinvest in the ex post SOLNG, SOLNU, .... Some deleveraging might be
advisable depending on the SOLNG productivity factor.
Statistics
Here are summary statistics for the experimental investment portfolios described
below. These statisics cover the
week period from
to
. The two green
portfolios had the highest Sharpe Ratios* over this period. Either of these
strategies should allow you to “beat the market and sleep well at
night.”
| Investment Portfolio |
FinalVal |
CmpdRtn |
StdvRtn |
ShrpRat |
Reinv |
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| * |
The long-term, compound-interest Sharpe Ratios in this table measure the ratio
of reward to risk, but they have a different scale than the short-term,
simple-interest Sharpe Ratios in the other parts of this study.
|
Investment portfolios
| SOLNG
| Modeled on the ex post SOLNG portfolio.
Reinvest in the ex post SOLNG portfolio whenever the Sharpe Ratio of your
investment portfolio is
off from the optimal, ex post SOLNG Sharpe Ratio.
Use the Portfolio Calculator to determine when such reinvestment is needed.
|
| SOLNU
|
Modeled on a constrained, ex post SOLNG portfolio.
About 1/3 of the (weekly) ex post Sharpe-optimal SOLNG portfolios since the
turn of the century were more than 70% in one fund. The SOLNU allows at most
70% in one fund (unless the SOLNG Sharpe Ratio is negative, in which
case both SOLNG and SOLNU consist of the one fund with the highest Sharpe
Ratio).
The SOLNU investment strategy reinvests in the ex post SOLNU portfolio
whenever the Sharpe Ratio of the current portfolio is
off from the ex post SOLNU Sharpe Ratio.
|
| SOLNL
|
Modeled on a constrained, ex post SOLNG portfolio.
The S&P 500 is weighted by market capitalization.
Financials (XLF) and Technology (XLK) account for roughly 20% each.
Consumer Discretionary (XLY), Consumer Staples (XLP), Energy (XLE),
Health Care (XLV), and Industrials (XLI) account for another 10% apiece.
Materials (XLB) and Utilities (XLU) make up the remaining 10%.
The Sharpe-optimal SOLNL portfolio makes a modest attempt to respect market
capitalization by requiring, at the very least:
XLF, XLK – 10%; XLY, XLP, XLE, XLV, XLI – 5%.
The ex post SOLNL portfolio adjusts the remaining 55% to produce the highest
possible Sharpe ratio.
The SOLNL investment strategy reinvests in the ex post SOLNL portfolio
whenever the Sharpe Ratio of the current portfolio is
off from the ex post SOLNL Sharpe Ratio.
|
| SOLNGD
| Deleveraged version of the SOLNG investment portfolio.
Reinvest whenever the Sharpe Ratio is
off, but deleverage by
max( 2 × pq, 0.20 )
when the productivity quotient, pq, of (ex post)
SOLNG is less than 0.5. (The productivity quotient of SOLNG is listed on the
Portfolio Calculator page.)
For example, if you are about to reinvest and the productivity quotient of
SOLNG is pq = 0.287, then cash in your chips
and reinvest 2 × 0.287 = 57.4% of your money in the SOLNG
portfolio and 42.6% in the base fund. On the other hand, if the productivity
quotient of SOLNG is 0.1 or less, put 20% of your money in the SOLNG
portfolio and the rest in the base fund.
|
| SOLNGB
| Same as the SOLNGD portfolio except that, in addition
to deleveraging, switch into or out of the base fund whenever the
-week
moving average of the SOLNG productivity quotient (image on the Portfolio
Calculator page) crosses the
level.
|
| SOLNGW
| Reinvest in the ex post SOLNG portfolio at the beginning of
each week.
|
| SOLS0
| A long-short investment portfolio modeled on the ex
post SOLS0 portfolio. Reinvest in the ex post SOLS0 portfolio whenever the
S0-ratio of your investment portfolio is
off from the optimal, SOLS0 S0-ratio. Use the Portfolio Calculator to
determine when such reinvestment is needed.
The S0-ratio is the Sharpe Ratio appropriate to the common situation
where short-money-received is held by the broker. The S1-ratio applies when
short-money-received can be invested in the base fund.
|
| SOLS0S
| Scaled version of the previous, SOLS0, portfolio.
Reinvest when S0-ratio of the investment portfolio is
from optimal, but scale the reinvestment by putting 100% of your money in the
long portion. Thus, if the ex post SOLS0 portfolio is 60% long and 40% short
and you have $100,000 to invest, put all $100,000 in the long shares and sell
$150,000 worth of shares short. The margin of 2/3,
| Margin = |
value of assets – loan |
= |
$250,000 – $150,000 |
, |
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| loan | $150,000 |
is well above the 50% minimum for short sales. The ex post SOLS0 portfolio
has always been at least 38% long over the period under consideration.
Scaling the long portion to 100% never produces an insufficient-margin
problem.
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| SOMIX
| The SOMIX investment portfolio is the long-short
analogue of SOLNGB. Instead of switching in and out of the base fund when the
-week
moving average of the SOLNG productivity quotient crosses
,
switch in and out of SOLS0S when this condition is met. The Sharpe Ratio
reinvestment triggers are still
and
for the SOLNG and SOLS0S portions, respectively.
|
Behavior of investment portfolios
SOLNG
The SOLNG investment portfolio outperformed the S&P 500 (as represented by SPY)
over the
weeks from
to
.
The annual rate of return of SOLNG over this period was
.
This compares with
for a 3-month-Treasury fund (the base fund) and
for the S&P 500 (SPY). SOLNG was a bit more volatile than SPY. The
annualized standard deviations of (compound) return were
and
,
respectively. SOLNG required a total of
portfolio reinvestments (including the initial investment) in the
weeks shown.
SOLNU
The constrained, SOLNU investment portfolio was able to outperform the S&P
500, but it substantially underperformed the unconstrained, SOLNG investment
portfolio.
SOLNL
The constrained, SOLNL investment portfolio was able to outperform the S&P
500, but it substantially underperformed the unconstrained, SOLNG investment
portfolio.
SOLNGD
The SOLNGD investment portfolio earned an annual rate of
over the same
weeks, compared with the
earned by the SOLNG portfolio. The final values, starting from a nominal
100.00, were
and
,
respectively. SOLNGD earned its keep with far less
risk, or volatility, than SOLNG. The standard deviation of return of SOLNGD
was only
,
roughly half of SOLNG's
.
This relative lack of volatility is apparent in the performance graph. Also,
the value SOLNGD only dropped to
(on
)
compared to SOLNG's nadir of
().
You might sleep better at night with SOLNGD.
SOLNGB
The SOLNGB investment portfolio out-performed SOLNGD over
the given period. It's return,
,
and final value,
,
were somewhat higher. It's standard deviation of return,
,
and minimum value,
,
(on
)
were about the same. The solid squares on the graph below are the
switch-points, where the
-week
moving average of the ex-post-SOLNG productivity quotient crossed the
level.
The ex-post-SOLNG productivity quotient and its
-week
moving average over the period under consideration are pictured below. The red
line indicates the
-week
switch-level for SOLNGB and SOMIX. Long reinvestments (in the
SOLNGD, SOLNGB, and SOMIX investment portfolios) are not deleveraged when the
productivity quotient is above the dotted 0.50 level
SOLNGW
In the previous strategies we reinvested only when the Sharpe Ratio
diverged from that of the ex post SOLNG model by
(except for switching in
and out of the base fund in the SOLNGB portfolio). On average a bit over three
reinvestments per year were required. Each investment portfolio handily beat the
large-cap benchmark SPY.
Obviously our investment costs would increase substantially if we were to
reinvest in the ex post Sharpe-optimal allocation every week. However,
regardless of the additional cost of investment, such frenetic trading produces
relatively poor results. This is evident in the graph of the SOLNGW investment
portfolio below.
The SOLNG investment portfolio is included in the picture for comparison.
The large dots on its graph are its
reinvestment points. The SOLNGW investment portfolio has
reinvestment points (not shown), one for each week.
SOLS0
It is clear from the picture below that the SOLS0 investment portfolio
is particularly effective at hedging risk. Indeed its standard deviation of
return was only
over the period under consideration. Unfortunately its annualized compound
return,
,
was also quite modest.
SOLS0S
The SOLS0S investment portfolio looks pretty much like SOLS0 but with
increased volatility. It's standard deviation of return was
and its annualized return
.
Both SOLS0 and SOLS0S required
reinvestments over the
weeks.
SOMIX
The SOMIX investment portfolio,
with a final value of
,
is the most spectacular of
the portfolios we consider. Over the
weeks it earned an annualized
with a standard deviation of return of
.
The squares show where the SOLNG/SOLS0S models were switched. These switches
are included in the
reinvestments required by SOMIX. The nadir of SOMIX was
.
This occured on
.
Historical data
The experimental, investment portfolios above are modeled on weekly, ex post
Sharpe-optimal portfolios. The zip archive
spdrPortf2-3mB.zip contains complete, comma-separated-value
(spreadsheet) data on the ex post portfolios going back to 17-Dec-1999.
The zip archive
portfHistory.zip
contains the composition, from week to week, of the SOLNG, SOLNGB, and SOMIX
investment portfolios going back to 3-Jan-2000.
The values of the investment portfolios from week to week
depend first-business-day adjusted-closing-prices and 3-month Treasury bill
rates. These data can be found at
<
http://finance.yahoo.com/>
and
<
http://federalreserve.gov/Releases/h15/data.htm>,
respectively.
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