Rainbow Curve

As I mentioned earlier the highest I have been on land was on Trail Ridge Road in Colorado. The photo was taken from the Rainbow Curve in August 1994. Trail Ridge Road tops out at 12183 feet but Rainbow Curve is at a mere 10875.

Solar vrs Wind

My last tirade about rooftop photovoltaic installations prompted a request for alternative suggestions.

The problem with rooftop solar photovoltaic electricity generation is that it costs too much. According to this a 4 KW rooftop photovoltaic installation costs $32000 or $8000 per KW. By comparison a 1.5 MW GE wind turbine like those in the Walnut Wind Farm appears to cost about $3000000 or $2000 per KW. So the wind turbine is 1/4 the cost per KW. It can be expected to have a better capacity factor as well. Note rooftop solar in particular will often have a lower capacity factor because of unfavorable location or orientation. So wind is much cheaper.

The above figures are rough estimates. For a sanity check see this account of a HSBC investment report which says in part:

What’s really interesting about HSBC’s new report is how solar power stacks up today against other ways of generating electricity—it doesn’t. That is, all the other power-generation technologies are in roughly the same neighborhood, even wind power—but not solar.

For instance, HSBC estimates costs per megawatt for different options: Combined-cycle gas, 43 euros; regular coal, 62 euros; onshore wind, 58 euros; nuclear power, 48 euros; geothermal, 43 euros. Photovoltaic solar power costs 290 euros per megawatt; concentrated solar power 181 euros.

Again wind power is much cheaper than photovoltaic solar power. In fact if we ignore the fact that wind is intermittent it is competitive with fossil fuels.

So wind is real, rooftop photovoltaic is just symbolic.

Yankees clinch

The Yankees clinched the American League East last weekend sweeping their arch rival Boston Rex Sox in the process. As I mentioned at the start of the season I am not much of a baseball fan but I do follow the Yankees a little.

With the baseball season winding down the standings will start containing the "x"s and "y"s denoting teams that have clinched spots in the post season or division titles. Another feature I would like to see in the standings is an indication (possibly a line through the team name) of which teams have been mathematically eliminated from post season play. Unfortunately I expect the papers are wary of probable league public relations objections. And of course it would be a little tricky to determine exactly when teams are eliminated in some cases. Still I think it would be interesting.

Mathematics

I was asked in comments a couple of days ago whether I was doing mathematics while out of work. Somewhat sad to say, the answer is no or at least not seriously. While with my former employer I gradually did less research level mathematics until in the final years I was doing programming almost exclusively. So at this point I am rather out of touch with the current research and am not very motivated to get back into it.

Some people can work for years on a problem without much interaction with other people. I am not really able to do this. So as I gradually lost contact with the mathematics research community I became less productive. And I became more interested in other things.

Vaccine trial statistics

The US military has been conducting a large and expensive AIDS vaccine trial in Thailand. Recently positive results were announced with much fanfare .

However the actual results are not that impressive. 74 out of about 8000 in the placebo group became infected as opposed to 51 out of about 8000 in the vaccine group. An approximate test of significance is to ask if we flip a fair coin 125 times what percentage of the time will the head tail split be at least as uneven as 74/51. By my calculation 4.87%. So this is statistically significant at the 5% level but just barely so. Again by my calculations if there had been one fewer infection in the placebo group this value would have been 5.89% or if there had been one more infection in the vaccine group this value would have been 6.09% neither of which would have been significant.

This illustrates one of the problems of picking an arbitrary line like 5% and declaring results on one side successes and on the other side failures. Another problem is the fact that there have been many vaccine trials other than this one all of which failed. Clearly if you run enough trials some will appear to succeed (at the 5% level) just by chance. I think there is a fair chance this is an example.

Pension finalized

Last week I sent in the forms to initiate my pension. As discussed earlier I chose to receive it all in the form of a single life annuity. I called today and verified that the forms had arrived ok. So I am all set to begin receiving a pension in November (although the first payment may be delayed a little).

Traditional defined benefit pensions like mine are becoming less common especially for private employers. Defined contribution plans (eg 401k) are becoming more popular. And in fact my former employer had shifted during the time I worked there, first putting all new employees into a 401k plan and later terminating the traditional pension plan (while preserving benefits earned). I think the main reason for this is that the value of a 401k plan is more apparent to employees. Each year you see how much money is added and the accumulated value. And it is totally portable. By contrast I expect most employees have little idea how to value a traditional pension. Since traditional pensions are in fact quite costly for employers this makes them an undesirable form of compensation.

One liberal complaint, which getting laid off has made me a bit more sympathetic to, is 401k plans and the like require people to be investment managers a task that many people are likely to be bad at. I am smart and fairly knowledgeable about financial markets and I still find managing my 401k and other investments a bit daunting. I expect many people would make expensive mistakes.

I consider this a strong argument against privatization of social security. Social security is not all that generous but it does provide a safety net. Left totally to their own devices I expect many people would end up worse off.

Black-Scholes

One thing I didn't like about "Panic" was the introduction by Michael Lewis which contained a confusing and in my view wrongheaded attack on the Black-Scholes option pricing formula.

Briefly Black and Scholes showed given a certain simplified model of the world in which stock prices move in continuous random walks then you could derive a formula for the value of stock options. Now it has always been known that this simplified model was not completely accurate. This is generally the case with models. The real world is very complicated and hard to understand. So we look at simplified models of the world which we can analyze. If chosen carefully such models can give us considerable insight into what is happening in the more complicated real world. But they will never match reality exactly and will increasingly diverge from reality as we move into domains where the simplified model assumptions break down. Still such models can be very useful.

But Lewis writes:

... At the end of 2006, according to the Bank for International Settlements, there was $415 trillion in derivatives-that is, $415 trillion in securities for which there is no completely satisfactory pricing model. ...

This is a silly objection. There is no completely satisfactory pricing model for stocks so why should there be one for stock options? In both cases the price is ultimately determined by the market, by the balance between supply and demand. The market price can be very wrong in retrospect. For instance during bubbles. But this is not the fault of the Black-Scholes formula. It just reflects the fact that it can be hard to think independently from the herd.