August 2008


Bill Rempel has a post up regarding the Sharpe Ratio, which I quite liked as far as it went. The only problem is that I think Bill must be a fairly advanced statistician as many of his concepts stated, but not elaborated on. For systems testers, there could be some interesting lessons hiding in there. Today will therefore be Statistics Sunday.

When one is evaluating systems (or a manager), it’s advisable to measure both the return and the risk associated with it. Often the volatility of the return stream, which isn’t necessarily the same thing as its risk, is thought of as synonymous with risk and substituted for risk in the measurement. The Sharpe ratio is one metric often used for measuring return in relation to risk; the Sortino ratio is another.

We have a number of concepts here, volatility, risk, Sharpe ratio, Sortino ratio. Fuzziness predominates when many of these concepts are discussed.

Volatility is defined as the Annualized Standard Deviation. What then is the Standard Deviation?

Standard Deviation is a measure of the dispersion of a set of data from its mean. The more spread apart the data, the higher the deviation. Standard deviation is calculated as the square root of variance [variance being defined as measure of the dispersion of a set of data points around their mean value. Variance is a mathematical expectation of the average squared deviations from the mean]

You see, we’ve hardly even made it out of paragraph one, and already it’s getting a little fuzzy. The point of the original article was to shed light on the fact that the Sharpe ratio, that appears all over the place can be rather misleading unless you really understand the nuts & bolts. We move on.

(1) Maximizing the Sharpe ratio maximizes compounded returns.

Only if the distribution of returns is symmetric. Are returns distributed symmetrically? Not in THIS universe. To paraphrase Rodney Dangerfield’s character in “Back To School,” speaking to his business professor, maybe we should base our funds in Fantasyland, home of exclusively Gaussian distributions!

Compounded returns are also known as “Geometric Returns” which are, or can be confused with “Arithmetic Returns.” This difference plays havoc with actual dollar returns, so you need to be careful. This is all based on a chap named Bayes, who postulated this hypothesis as his PhD. The average annual returns [arithmetic] over the five years was 10% (15% + 0% + 20% – 5% + 20% = 50% ÷ 5 = 10%), but the compound annual growth rate (CAGR, or geometric return) is a more accurate measure of the realized gain, and it was only 9.49%. Volatility eroded the result, and the difference is about half the variance of 1.1%.

Notice that volatility increases as the interval increases, but not nearly in proportion: the weekly is not nearly five times the daily amount and monthly is not nearly four times the weekly. We’ve arrived at a key aspect of random walk theory: standard deviation scales (increases) in proportion to the square root of time. Therefore, if the daily standard deviation is 1.1%, and if there are 250 trading days in a year, the annualized standard deviation is the daily standard deviation of 1.1% multiplied by the square root of 250 (1.1% x 15.8 = 18.1%). Knowing this, we can annualize the interval standard deviations for the S&P 500 by multiplying by the square root of the number of intervals in a year:

Returning to Bill and Gaussian distributions, I have written many times that the Gaussian distribution in the stockmarket is pure nonsense and tantamount to potentially blowing-up your account. We also have a second component hiding in there which is critical to any Gaussian distribution, the “Random Walk.”

The Random Walk mandates “independence.” That is to say, one price change in a stock, is totally unrelated to a previous price change [in any timeframe] in the same stock. That the next price quoted is random, like the flip of a fair coin. You need only study momentum traders, or various theories on chart patterns to understand that this is pure nonsense; price change in one direction, will attract further participants to the trend developing.

Therefore, we can state that a Gaussian distribution should not exist in the financial markets. Let’s examine the data.

We can observe two differences between the normal distribution and actual returns. First, the actual returns have taller peaks – meaning a greater preponderance of returns near the average. Second, actual returns have fatter tails. [kurtosis] Taking -3 Standard Deviations as a large loss, the Gaussian curve predicts such a loss would occur approximately 3/10 years. The actual loss occured 14/10 years.

These results are within the S&P500 & NASDAQ index, thus diversification damps the volatility or standard deviations. If we look at individual stocks that make up those index, we see an increasingly non-Gaussian distribution in the 1999 data.

Total Stocks………..3SD………..4SD……….5SD……..6SD………Total……2466
Up move……………..309………..116……….44………..47………..516…….20%
Down move………….69………….29………..15………..19………..132…….5.3%

The lognormal distribution, or Gaussian distribution states that a stock really can’t move more than 3SD in any timeperiod, obviously, simply incorrect.

(2) The Sharpe ratio measures the probability that a given return stream is significantly different from the “Risk Free” rate of return.

A ratio developed by Nobel laureate William F. Sharpe to measure risk-adjusted performance. The Sharpe ratio is calculated by subtracting the risk-free rate – such as that of the 10-year U.S. Treasury bond – from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns.

Obviously there is the already highlighted problem of volatility not conforming to a standard distribution. There are additional problems however [should you still be intent on using the Sharpe Ratio]

As the above table shows, zero or constant volatility demonstrated in a falling graph can actually be reversed and show a very high Sharpe Ratio. Take as an example a Hedge Fund that “Sells Premium” as an example, in a trending market as we had from 2003 to 2007, this strategy might well have exhibited a very high Sharpe Ratio;

For example, according to Hal Lux in his article, “Risk Gets Riskier”, which appeared in Institutional Investor in 2002, Long-Term Capital Management (LTCM) had a very high Sharpe ratio of 4.35 before it imploded in 1998.

An area not touched on by Bill with regards to the Sharpe Ratio, is one of liquidity. Liquidity was an issue with LTCM, and more recently, it has been a massive problem for the Banks, Hedge Funds, Insurance Companies, Municipalities and generally anyone holding Mortgage Backed Securities [MBS]

The totally illiquid market for MBS has caused massive Mark-to-market losses for all concerned. Losses in excess potentially of the actual default rate. Of course, prior to the debacle, Sharpe ratios again will have shown high values.

The Sortino Ratio is a ratio developed by Frank A. Sortino to differentiate between good and bad volatility in the Sharpe ratio. This differentiation of upwards and downwards volatility allows the calculation to provide a risk-adjusted measure of a security or fund’s performance without penalizing it for upward price changes. It it is calculated as follows:

The Sortino ratio, as can be seen only utilises “downside volatility” in the denominator. Returning to our prior definitions of volatility, one must ask, if volatility has been discredited as a metric based on a Gaussian distribution, how accurate then is the ratio for describing risk based on a metric of volatility?

Which really opens up an entirely new discussion on how to actually define “RISK” as we can see volatility, while one of the numbers, does not fully describe risk accurately.

Another blogger [trader] bites the dust. Daytrading is not an easy game. Having followed this blog off and on for about a year, what went wrong? Basically he had one strategy, and that strategy did not gell with his psychology, thus the emotional strain was immense, hence burn-out.

The answer would have been to find a trading methodology that sat easily with his psychology and developed a winning expectancy around that.

I am going on vacation for a week. When I come back I do not know if I will continue trading or not. If or when I next trade, I do not know if I will post my results. Maybe I will just post my market thoughts from time to time.

I did not blow up. In fact I am up a small amount for the year and made 4k last year and 7k the year before. It is the fact I am getting no where while I have been at this full time for nearly a year and it is frustrating the shit out of me where I can no long function. Something has to change before I do something really stupid.

Good Bye until next time.

Percentage of Stocks Above Moving Average
……………………20-Day……….50-Day……..100-Day………150-Day……200-Day
Today…………….56.86%…….. 57.23%……. 37.15%………. 35.21%….. 32.58%
Yesterday ……….62.98%……… 58.88%……. 38.64%……… 36.83%…… 34.06%
Last Week……… 52.94%…….. 49.83%…….. 35.35%……… 34.39%…… 31.40%
Last Month……… 60.71% …….32.97%…….. 29.56%……… 28.95%…… 25.61%

Herein lies the problem with chart analysis, I could argue a plausible case for either Bull/Bear cases based on the preceeding charts, depending on any biases I might hold. My bias is for the Bear case based on the economy, but, I could quite easily entertain, based on the charts an optimistic outlook.

Based on market valuations, we are nowhere near a major market bottom. I would be a buyer if we were at a major bottom, irrespective of the fluctuating news flow, but, as stated, the valuations are still far too high.

Can we bounce? Absolutely. As my water indicates, such a bounce might be underway currently. The most bullish chart the P&F, would suggest also an upcoming bounce. The market internal data has described a short-term bottom as % of stocks seem to be climbing back above all their moving averages currently.

The question seems to be; will this be a 1968 -1982 Bear market, or a 1990 -1991 Bear market? The difference is obviously significant.

By Jon Markman
Not too long from now, a sensuously curved sports car designed by a German and made with American parts will roll off an assembly line in Finland and quietly mark the first clear break from our century-old dependence on crude oil for transportation.

Many a dreamer has attempted to create a serious, reasonably priced automobile that sidesteps oil and gas as an energy source, but all have flopped and sent investors straight to the poorhouse. Yet this one really has a shot at success, not just as a science experiment but as a commercial endeavor that could provide the first independent rival to the big international automakers in decades.

The new vehicle, the Fisker Karma, is the result of a marriage of convenience between art and commerce — the love child of idealistic former BMW designer Henrik Fisker and Silicon Valley venture capitalists eager to make a smart, early bet on alternative energy.

4 cents a mile
Although the car looks like sex on wheels, with a long, swoopy hood and flared-out wheels, it is a marvel of engineering that re-imagines the automobile from the power plant to the solar-panel roof for an era when cheap, clean, plentiful electricity will push expensive, filthy gasoline to the sidelines. It’s ready to roll for around 4 cents a mile.

The power for the Karma comes straight from a standard electrical outlet, no fancy charging apparatus required. And unlike the Toyota Prius, the hybrid gas-electric darling of the eco-friendly set today, the Karma could run its entire life without ever sniffing gas.

For while the dirty secret of the Prius is that it’s powered by a conventional internal-combustion engine that switches to electrical power in low-demand situations, the Karma is an electric vehicle that requires only a short recharge boost from its small gas engine if traveling 50 miles from its base.

The Karma is to go into full production next year.
The big idea behind the Karma, which will initially cost $80,000 while in limited initial production, is that the best alternative to crude oil for transportation is not a new fuel or technology but simply efficiency. The genius is that it transforms electricity generated by anything ranging from a home solar-panel system to a utility company’s wind turbines into a fuel that can power a strong, safe, well-appointed, roomy car on the average commuter’s trek to work and back.

In fact, if you’re among the 60% of the U.S. population that drives less than 25 miles each way to work, you may never have to buy gasoline again. If you do decide to take it out on the open road for a trip across the state, this plug-in electric hybrid vehicle, or PHEV, will get about 100 miles to the gallon — at least double the Prius’ fuel efficiency. That’s not bad for a car rated to jump off the line to get to 60 mph in 5.8 seconds.

Less battery, more space
PHEVs are much more efficient than their gas-powered cousins because electric motors are better at turning a single Btu of energy into motion, in part because they produce no wasted heat themselves. They’re also better because we have many more low-emission, U.S.-based ways to produce electricity — natural gas, solar, nuclear and wind, for example — than we have sources for liquid fuels.

The problem with electric-car motors up to now has centered on the batteries. Laws of physics make it hard to create batteries that hold a big enough charge to provide a lot of juice and are still light, small and safe enough to fit into a passenger vehicle without compromising fit and finish. The densest batteries, which provide the most juice, also tend to require the longest recharge times.

A Karma competitor called the Tesla Roadster, which will go on sale soon, is so optimized to go distances of up to 200 miles on a single charge that its battery is huge and surrounded by a water-based cooling system. As a result, the Tesla holds only two people and little luggage. In contrast, the Karma, using lithium-ion manganese batteries, is optimized for the 50-mile range that is considered to be the need of a majority of early adopters, and that’s why there’s room in the vehicle for four people to sit comfortably — and haul at least a couple of golf bags, to boot.

With the major automakers struggling, you might think that this is a dumb time to come out with a new car. But it may turn out to be quite the opposite. The automakers all have a lot of excess capacity on their factory floors now, and the same goes for suppliers of interiors, hoses, tires, suspension systems and other parts.

Instead of facing a quandary like that of John DeLorean — who was the last man to challenge the Big Three and who was ultimately crushed by the need to create every part in-house — a new automaker today can rely on just-in-time inventory systems to provide an efficient supply chain and can bargain with plant owners who are dealing with millions of hours of idle capacity. The Karma will be made at Valmut Auto in Finland in the same plants that today produce the Cayman and the Boxster for Porsche.

If you can’t buy, invest
David Anderson of hedge fund Palo Alto Investors, whom we’ve always known here as an oil and gas specialist, became an early investor in the Karma after looking for years at many other alternative-energy technologies, as did the major venture-capital firm Kleiner Perkins. Anderson said a smart investment in alternative-energy needs to fulfill all four of the following criteria: It must make good economic sense, it must reduce emissions, it must provide more energy for the growing worldwide economy, and it must reduce dependence on any single commodity.

Getting down to brass tacks, Anderson said his firm believes that if it can’t reasonably turn a $20 million investment into $80 million in five years, it’s not interested. It’s also not interested in solutions that don’t scale or in those that pollute or depend heavily upon government grants.

Most Americans don’t have $80,000 for the car or $20 million to make a venture-capital investment, but there is one potential common-stock investment in the Fisker: Quantum Technologies (QTWW, news, msgs), which makes the car’s Q Drive motor.

Quantum is a major supplier of clean-energy technologies to automakers and the military, so its plug-in hybrid electric motor for the Karma is the result of a long history of experimentation and production, not a one-off test case. With its stock now trading around $1.75 a share, Quantum’s revenues have been going downhill for years, and it’s never made a profit. But that could turn around if the Karma and other projects take hold in the marketplace.

This kind of idea is bound to provoke plenty of skepticism until it goes into full production in 2009 and begins to generate sales. But new solutions for a world of scarcer, more expensive energy have to start somewhere, so you can’t immediately dismiss every attempt as impossible.

Anderson said he’s involved because he “likes to know stuff before other people,” and if it turns out that PHEVs take hold at the lower price point of the Chevy Volt — scheduled for production in 2010 around $30,000 — then he’ll have an early view of the potential impact on his oil and gas exploration and services investments.

Ideally, it would be great to see PHEVs reduce demand for the foreign oil used in cars while increasing demand for the U.S.-produced natural gas used in electric utilities. That would be a win for the environment, energy independence and our portfolios.

From Bloomberg;

The meager gains in earnings over the last year signal the U.S. economy is in much deeper trouble than the growth estimates indicate, economists said.

Gross domestic income (GDI), or the money earned by the people, businesses and government agencies whose purchases go into calculating gross domestic product, rose 0.3 percent in the 12 months ended in June after adjusting for inflation, according to Bloomberg calculations based on today’s Commerce Department growth report. GDP expanded 2.2 percent.

“The income side of the economy, with profits down for four straight quarters and employment falling, looks like a recession,” said John Ryding, chief economist at RDQ Economics in New York.

Date (Month, Year)…………………………………July 2007…………July 2008
Index Price………………………………………………..1520.7……………1256.0
Dividends …………………………………………………..$26.44……………$28.98
Earnings……………………………………………………..$70.32……………$56.88
Dividend Yield (%) …………………………………….1.74%…………….2.31%
Price Earnings Ratio ………………………………….21.63……………..22.08
Consumer Price Index ………………………………208.3……………..216.3

Index Rate of Return without dividend…………………………………………….[-17.41%]
Index Rate of Return with dividends………………………………………………..[-15.74%]

Official Inflation Rate……………………………………………………………………….3.84%
Return after inflation w/o dividends………………………………………………..[-21.25%]
Return after inflation with dividends………………………………………………[-19.58%]

Price of Gold…………………………………………………$650……………….$850
Implied Inflation……………………………………………………………………………30.7%

Return after implied inflation w/o dividends……………………………………[-48.1%]
Return after implied inflation with dividends…………………………………..[-45.8%]

Now while I think the implied inflation via the price of Gold is somewhat optimistic, neither do I subscribe to the official rate of 4% odd. It is obvious however that earnings have fallen rather dramatically, collapsed might be accurate. Is this trend likely to continue into the immediate future? I would say yes, Europe is also having major problems, China, with no-one to export to is suffering a capitalistic bust, earnings are not likely to be growing anytime soon.

Today’s chart illustrates the Dow’s average performance for each calendar month since 1950 (blue columns) and 1980 (gray columns). What does the chart show? While the strongest upward bias in stocks has historically occurred during the November-January time frame, September has proven to be the most difficult month for stocks. It is interesting to note how the 1980-present average gain for September has remained negative despite the fact that most of this period included a strong bull market.

The general concensus seems to be that cost-push inflation will never become a threat. However, when any topic starts to enter the mainstream, as in the example of the cartoon, then things have a funny way of coming out of the woodwork.

NAIRU or, non-accelerating rate of inflation is the theoretical economic construct governing or relating to cost-push inflation. The basic premise is that an increase in demand can be translated into higher employment only up to the NAIRU limit. At that point, higher demand drives higher prices. This is an adjunct to Capacity Utilization, which relates to manufacturing capacity.

Thus it is easy to understand therefore that the establishment, economists, are in essence discounting any chance of a cost-push inflation as employment is currently falling. Would this therefore negate my advocacy, of the possibility of a cost-push inflation?

Let’s examine the historical data: First, the employment data;

This demonstrates the periods of high unemployment. Periods where according to the “Phillips Curve” wages should remain constant, or even fall, due to the NAIRU theory.

Here then is the wages data;

Clearly we can see that the decade of the 1970’s was marked by higher wages, with lower employment. Any guesses as to inflation at these times? Of course, the highest inflation in modern times within the US

Year……………Inflation Rate
1970……………… 5.92
1971……………… 4.30
1972……………… 3.31
1973……………… 6.21
1974……………. 10.98
1975…………….. 9.14
1976……………. 5.76
1977……………. 6.45
1978……………. 7.61
1979………….. 11.27
1980………….. 13.52

Next Page »