Browse Author by Qiao Zhou

Conservation of Energy: Theory and Applications in Finance

1. Theory of Conservation of Energy

According to the theory of conservation of energy, the total energy of a closed system remains constant, although the form of energies can be converted from one form to another. Most of the ideas in this article are inspired by the discussions made by the grandmaster of trading, Mr. Victor Niederhoffer, in his book ‘Practical Speculation’ (Victor Niederhoffer, 2005). Any valuable insights belong to him, and I’m responsible for any mistakes made.

2. Applications in Finance

2.1. When Number of IPOs Declines

Under the thinking framework of conservation of energy, we assume that the capital available to invest in stocks are constant over time. Since money invested in stocks can either be invested in the form of existing stocks or new initial public offerings, these two quantities are expected to be negatively correlated. We further claim the hypothesis that when more money is invested in IPOs, less money will be available to invest in existing stocks in subsequent period. If this theory really holds, then their correlation should be expected to be around -0.7[1].

Statistically, the test shows that declines in annual IPO offering numbers are highly bullish for the stock market returns next year. Concretely, the Historical monthly US IPO Statistics data from 1960 to 2014 provided by Professor Jay Ritter in University of Florida is used for constructing the regression and correlation test. The correlation between the gross number of IPOs (the gross count, which includes penny stocks, units, closed-end funds, etc.) of the current year and the S&P return of the next year is -17%, and the least square regression shows a regression relationship of: chg_S&P = 10.15 – 0.03 * chg_IPO.

Therefore, if the number of IPOs decrease by 50%, then the next year stock return is expected to increase by 1.5%. A scatter plot together with a regression line is plotted below for ease of illustration:

sp_ipo_scatter — Change in Number of IPO This Year v.s. S&P Return Next Year

2.2. Equity/Money-market Ratio

When more money is moving from equities to money-market funds, it suggests a good time to buy equities. Low level of equities/mm ratio suggests a higher than average monthly returns in equities market. I will test it in a later post.

Bibliography

Victor Niederhoffer, L. K. (2005). Practical Speculation. Wiley.

[1] Assuming X is the dollar amount available to buy initial public offerings, Y is the total dollar amount available to buy stocks, and then the amount available to buy existing stocks is Y-X. Assuming X and Y are uncorrelated with equal variance, then it can be shown that, which is approximately -0.7

Opinions

Some Insightful Quotes

Self-Discipline

What lies in our power to do, lies in our power not to do. (Aristotle)
We don’t have to be smarter than the rest. We have to be more disciplined than the rest. (Warren Buffett)
A journey of a thousand miles begins with a single step. (Lao Tzu)
Rule your mind or it will rule you. (Horace)
The difference between successful and very successful people is that the latter say no to almost everything. (Warren Buffett)

Life

Success is getting what you want;happiness is wanting what you get. (Dale Carnegie)
Be the change you wish to see. (Gandhi)
My life is my message. (Gandhi)
Humility is not thinking less of yourself, humility is thinking yourself less.

Perseverance

If you’re going through hell, keep going. (Winston Churchill)

Investing

I’ve found that the big money was never made in the buying or the selling. The big money was made in the waiting.
You need discipline, patience, and courage. You must have a willingness to lose, but a strong desire to win.
The key is to lose the least amount when you are wrong. (William O’Neil)
There are two concepts we can hold to with confidence: – Rule No. 1: Most things will prove to be cyclical. – Rule No. 2: Some of the greatest opportunities for gain and loss come when other people forget Rule No. 1. (Howard Marks)

Factor Investing

Empirical Study of Value and Momentum Portfolio Returns

Factors are return drivers that carry intrinsic risk. Macro risk factors capture non-diversifiable risks that have exhibited positive expected returns over long run. Such risk factors include economic, real rats, credit, liquidity, inflation and emerging market, etc. (Ang, 2015). An investor holding bonds expose him to the risk of inflation and real rates hike, and is thus compensated for bearing such risks. Another source of return and risk are style risk factors. Such factors (e.g., value, momentum, earning quality, size, volatility, carry, curve, convexity, etc.) capture risk premiums that have been historically positive if held for long term.

I conducted empirical studies on the performance of investment strategies employing various quant equity factors during 1990 to 2016, and statistically significant anomalous profits are found for trading value, momentum, low-volatility and low-liquidity (Roger G. Ibbotson, 2013) portfolios. The main dataset used in the study is the stock return data from the CRSP database and the data available at Ken French’s data library[1]. In this section, we will cover mainly the empirical results of value and momentum portfolio during 1990-2005 and 2012-2016.

Value Portfolios

Investors seek value premium by holding high book-to-market ratio (B/M ratio) firms. The failure of CAPM to explain the returns of value/growth stocks is known as Value Puzzle. Empirically, value stocks outperform growth stocks in general. According to CAPM, the only factor impacting asset returns is beta, and difference in asset returns should be explained entirely by beta spreads. However, the beta spreads are found to be not distinguishable among value and growth portfolios, while their return expectations are significantly different. This is a challenge for CAPM. During 1990 to 2005, value portfolios[2] outperformed growth and market portfolios, in both absolute and risk-adjusted basis, by 2.05% annually. However, the recent performance of growth portfolios during 2012-2016 outperformed that of value portfolios by 1.24%. In addition, the growth portfolio used to be more volatile with larger maximum drawdown compared with value portfolios during 1990-2005, but it turns into a safer strategy with less drawdown during 2012-2016. These characteristic changes all suggest a potential regime change and factor rotation.

Portfolio Construction Methodology: Every June, we sort firms according to their B/M and form 3 portfolios: Value portfolio is constructed using the firms whose B/M ratio is ranked in the highest 30%, Growth portfolio is constructed using companies whose B/M ratio is ranked in the lowest 30%, and Neutral portfolio is constructed using the remaining 40% of firms. The return from July to following June is computed for each of the three style portfolios, and firms are resorted according to the current B/M to form three new style portfolios. This process is conducted from 1990 to 2016, and finally, the cumulative returns of each style portfolio are computed and compared against the returns of the market portfolio. The market portfolio return is obtained by adding back the risk free rate to the market risk premium factor used in the Fama French 3-factor model. All data used in this analysis is obtained from Ken French’s Data Library.

Value Growth Styles Summary, 1990-2005

STYLE	MEAN	STD	SHARPE	MAXDD	SKEW	CORR
Growth	11.13	16.01	0.44	65.24	-0.39	0.98
Value	13.18	13.75	0.67	33.41	-0.63	0.82
Market	11.24	14.78	0.49	55.65	-0.59	1

Value Growth Styles Summary, 2012-2016

STYLE	MEAN	STD	SHARPE	MAXDD	SKEW	CORR
Growth	14.98	11.53	1.3	8.95	-0.29	0.98
Value	13.74	12.74	1.08	15.14	-0.32	0.92
Market	14.16	11.36	1.24	9.11	-0.31	1

Momentum Portfolios

Momentum effect is more significant than value/ growth, but it can occasionally be trapped at crashes, while value/ growth effects are more stable. Compared with Value and Growth portfolio, momentum (i.e. winner) portfolios[3] have historically provided more significant abnormal returns, which is unexplainable by CAPM. Concretely, from 1990 to 2005, winner portfolio have generated on average 19.49% return annually with a Sharpe ratio of 0.71, skewness of -0.3, excess kurtosis and correlation of 0.81with the market portfolio[4]. In contrast, loser portfolios generated only 2.58% annual return with a Sharpe ratio of -0.05. One can also construct a market neutral winner minus loser (W-L) portfolio, which will generate 16.92% annually with a -0.18 correlation with the broad market. However, such momentum portfolio would have incurred a 60.66% maximum drawdown, which is too risky to be included in institutional quality investment programs. These drawdown episodes of momentum strategy are characterized as momentum crashes, which are usually observed during stressful periods and equity bubbles. During the bullish run of 2012-2016, momentum portfolio continued to be a strong performer. However, given the high valuation of the equity market, increased negative skewness and increased average correlation with the market return, one trading such strategy should be cautious about the systematic risk of a sharp equity drawdown.

Portfolio Construction Methodology: Momentum portfolio is constructed by sorting stocks according to returns over past 12 to 2 months to form deciles. The top 10% firms are purchased into the momentum (winner) portfolio, and the bottom decile firms are purchased into the loser portfolio. This rebalance is performed at the end of each June.

Momentum Deciles Monthly Summary, 1990-2005

DECILES	MEAN	STD	SHARPE	MAXDD	SKEW	CORR
‘Low’	0.21	8.47	-0.05	100	0.33	0.77
‘Dec_2’	0.77	6.3	0.24	76.63	0.05	0.8
‘Dec_3’	0.76	5.11	0.29	69.26	0.04	0.8
‘Dec_4’	0.93	4.44	0.47	43.3	-0.21	0.82
‘Dec_5’	0.72	3.97	0.33	26.95	-0.55	0.85
‘Dec_6’	0.83	3.94	0.43	44.49	-0.45	0.84
‘Dec_7’	0.96	3.91	0.55	26.13	-0.32	0.83
‘Dec_8’	1.19	3.85	0.77	27.83	-0.23	0.87
‘Dec_9’	1.05	4.17	0.6	29.72	-0.25	0.86
‘High’	1.62	6.29	0.71	60.66	-0.18	0.81

Momentum Deciles Monthly Summary, 2012-2016

DECILES	MEAN	STD	SHARPE	MAXDD	SKEW	CORR
‘Low’	0.5	7.18	0.24	50.4	-0.23	0.72
‘Dec_2’	0.59	4.9	0.41	28.73	-0.29	0.83
‘Dec_3’	1.04	4.14	0.87	17.89	-0.29	0.88
‘Dec_4’	1.16	3.37	1.19	10.46	-0.43	0.94
‘Dec_5’	1.45	3.53	1.42	8.95	-0.19	0.96
‘Dec_6’	1.17	3.23	1.26	8.02	-0.33	0.96
‘Dec_7’	1.28	3.16	1.4	8.87	-0.43	0.96
‘Dec_8’	1.31	2.89	1.57	9.68	-0.36	0.93
‘Dec_9’	1.36	3.29	1.43	8.75	-0.11	0.89
‘High’	1.56	3.9	1.38	10.05	-0.27	0.82

[1] http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

[2] The value/growth portfolio construction methodology can be found in Appendix B.

[3] The momentum portfolio construction methodology can be found in Appendix B.

[4] Market portfolio return is obtained by adding risk free rate back to the excess return used in the Fama French 3-factor model.