September 28, 2012 Update

    Cash:                             $ 13,486.80
    Accrued Dividends:                     170.20
    Stocks:                            113,092.42
    Options:                           (10,889.64)

  Account Value:                      $115,859.78

  Equity:                             $126,758.40
  Margin Requirement:                   73,386.51
  Available Funds:                      53,371.89

  Regulation T Margin Requirement:     100,002.19
  Special Memorandum Acct:              43,539.31

On September 29, a $172.00 dividend was paid for 400 shares of ARCC; $2.00 was paid for 200 shares of CSE; and $10.00 was paid for 100 shares of FTR.

The account value of $115,859.78 compares with the value a month earlier of  $114,037.23, a return of 1.60%. This compares, however, with the change in the S&P 500 Index from 1,406.58 to 1,440.67. Adding an estimate of a quarter percent dividend payment (one twelfth of 3%), this gives a return of 2.67% for the S&P 500, so my portfolio underperformed the market in the month of September. This is not too surprising to me because the market did very well during the month, and my strategy is designed to start to bail out when the market does particularly well.

Understanding Utility Theory

Uncertainty and risk have long confounded human reasoning: the syllogisms of basic logic assume certainty in all assertions, and allow no conclusions to be drawn until all factual states are decided.

And, in practice, people often demonstrate themselves to be remarkably poor at making decisions based on uncertain conditions, foregoing much needed insurances while over-paying for absurdly unlikely coverage, for example.

Within this confusion, the intuitively appealing notion of a "risk premium" has arisen. In general, the notion of a risk premium is that reasonable people will not accept risk without an expectation of, on average, profit above and beyond what is available without risk.

Utility theory is a method of quantifying the notion of a risk premium.

The main premise of utility theory is that we should concern ourselves not with the cash value ("wealth") of anything, but rather with the utility (which I guess is just a of saying "usefulness" with a word derived from Latin ...) of the wealth. And then there are just two parameters that the utility function of wealth are held to have to satisfy: the utility of more wealth is always greater than the utility of less wealth; and the rate of increase of utility relative to wealth decreases as the absolute level of wealth increases.

Mathematically, these two properties are stated as follows:

1. dU/dW > 0; and
2. d²U/dW² < 0.

And this is really all that standard utility theory tells us.

There are, however, a couple more things to know about utility theory.

The first is that, in standard financial theory today, utility theory is the beginning and end of how risk is understood. This can perhaps be seen most clearly through a 1963 article by Paul A. Samuelson, "Risk and Uncertainty: A Fallacy of Large Numbers", and through a 1995 article that is largely a reprise of the same argument: "On the Risk of Stocks in the Long Run" by Zvi Bodie (sorry, no link).

"Risk and Uncertainty" relies upon utility theory to demonstrate that if you will not accept, due to risk concerns, a single wager with a positive expected return, you also should not accept any multiple repetitions of the same wager, even if the possibility of any loss under the multiple repetitions is almost zero. "On the Risk of Stocks" uses Black-Scholes options pricing theory -- which is based on utility theory -- to dismiss the proposition that, if your time horizon is long enough, the higher expected return on stocks will make them a more suitable investment than investments with more certain returns, even though you would want the more certain investments for a shorter time horizon.

The second thing to know about utility theory is that it seems to have almost no predictive value whatever in determining how economic agents, like investors, actually behave. In traditional science, having no predictive value is the hallmark of a hypothesis (not a theory ...) that must be rejected.

September 26, 2012 Trade

Opened:
 Pos    Symbol                   Price     Comm       Net
 -2    BHP 16MAY13 45.0 P         1.05     0.76     (209.24)

September 25, 2012 Trade

Opened:
 Pos    Symbol                   Price     Comm       Net
 -3    JCI 19APR13 20.0 P         0.50     0.03     (149.97)

September 24, 2012 Trades

Opened:
 Pos    Symbol                   Price     Comm       Net
 -4    BMY 19OCT12 34.0 C         0.26     1.52     (102.48)

 -2    RIG 19OCT12 50.0 C         0.76     1.52     (150.48)

 -4    C 15MAR13 25.0 P           0.85     1.52     (266.48)

 -4    ABX 19APR13 30.0 P         0.70     3.04     (276.96)

 -2    DDS 17MAY13 60.0 P         2.95     1.13     (588.87)

September 21, 2012 Options Expirations and Update

Closed:
 Pos    Symbol                   Price     Comm       Net
 -4 BMY 22SEP12 34.0 C            0.00     0.00        0.00
     Basis 05/21/2012:                              (345.09)
     Profit/(Loss):                                  345.09

     Value 08/31/2012:                               (53.43)
     Post-August Profit/(Loss):                       53.43


 -2 RIG 22SEP12 50.0 C            0.00     0.00        0.00
     Basis 08/20/2012:                              (274.48)
     Profit/(Loss):                                  274.48

     Value 08/31/2012:                              (224.17)
     Post-August Profit/(Loss):                      224.17


 -3 CE 22SEP12 30.0 P             0.00     0.00        0.00
     Basis 02/23/2012:                              (222.94)
     Profit/(Loss):                                  222.94

     Value 08/31/2012:                                (3.72)
     Post-August Profit/(Loss):                        3.72


 -2 EMR 22SEP12 35.0 P            0.00     0.00        0.00
     Basis 03/23/2012:                               (89.35)
     Profit/(Loss):                                   89.35

     Value 08/31/2012:                                (0.01)
     Post-August Profit/(Loss):                        0.01


 -2 NSC 22SEP12 60.0 P            0.00     0.00        0.00
     Basis 01/23/2012:                              (418.94)
     Profit/(Loss):                                  418.94

     Value 08/31/2012:                                (0.59)
     Post-August Profit/(Loss):                        0.59


 -1 V 22SEP12 90.0 P              0.00     0.00        0.00
     Basis 01/23/2012:                              (533.97)
     Profit/(Loss):                                  533.97

     Value 08/31/2012:                                (0.00)
     Post-August Profit/(Loss):                        0.00

Also since the last update, effective September 20 a $170.00 dividend became payable for 1,000 shares of GE, and on September 21 a $142.01 dividend was paid on 400 shares of WM.

September 19, 2012 Trades and Update

Closed:
 Pos    Symbol                   Price     Comm       Net
 -4    GE 22SEP12 20.0 C          2.49     3.79    (2,493.79)
     Basis 01/20/2012:                             (1,002.74)
     Profit/(Loss):                                (1,491.05)

     Value 08/31/2012:                              (827.26)
     Post-August Profit/(Loss):                    (1,646.23)

Opened:
 Pos    Symbol                   Price     Comm       Net
 -4    GE 16MAR13 21.0 C          1.89     9.48    (1,880.52)

This pair of transactions was made in advance of an GE ex-dividend date of September 20, with a dividend amount of $0.17 per share.

Also since the last update, effective September 12 a $172.00 dividend became payable for 400 shares of ARCC and a $2.00 dividend became payable for 200 shares of CSE, and an $82.50 dividend was paid on September 12 for 300 shares of WAG.