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A Speculator's confessions of investing Taiwan stock index options

Chao-Hui Yeh

Associate Professor of Department of Business Administration

I-Shou University, Taiwan, ROC

TEL: +886-7-6577711 ext 5914 E-mail︰chy@isu.edu.tw

Abstract

This paper tells you my returns in the Taiwan stock index options (hereafter TXO). TXO is issued by Taiwan Index Futures Exchange (hereafter TAIFEX) based on Taiwan Stock Exchange Capitalization Weighted Stock Index (hereafter TAIEX)

From this paper you will know my trading strategy (behavior) in TXO. , which comprises puts & calls. In TXO, I most often sell out-of-the-money puts (hereafter puts) and most often sell out-of-the-money calls (hereafter calls). Selling put giving me the best returns, while selling call giving me the second best returns. Because I never sell or buy in-the-money puts or calls, in this paper all puts / calls are out-of-the-money. In TXO, I either sell and hold till to expires or buy back to offset (close) positions If I sell TXO (puts / calls) and hold till to expire, the closing trade that completes this round trip is to exercise the option at maturity (paying the intrinsic value of the option at maturity, if it is in the money).

On average I win after transaction costs are taken into account from trading options, even only I use the simplest trading strategy -- sell TXO. Based on the logistic regression, the main conclusion is that selling index puts will win most likely for all the bull/bear market condition.

Keywords: Taiwan stock index options, out-of-the-money puts, logistic regression

1. Introduction

Investors are generally divided into three categories: speculators, hedgers and arbitrageurs, these three types use different trading strategies.

If that hedgers buy insurance is truth, then speculators should profit and hedgers should lose averagely.

This paper is my returns in the TXO, meanwhile maybe also is the first empirical study of a speculator's trading strategies and profits in the TXO. And I am that speculator, so this paper is a speculator's public statement. TXO is a quite risky gamble.

My dataset is my transaction record from 2003.09.15 to now.

In my dataset, I use [pic] to stand for exercise price, [pic] to stand for underlying assets price, [pic] to stand for intrinsic value for put before settlement date, [pic] to stand for intrinsic value for put on settlement date, [pic] to stand for intrinsic value for call before settlement date and [pic] to stand for intrinsic value for call on settlement date.

Most existing studies analyze investors' portfolios at monthly or quarterly intervals, while my data is at daily intervals.

TAIEX is 30% of volatility yearly in return with a daily return is between -0.07 and 0.07. While S&P 500 is 13% of volatility yearly in return with a daily return is between -0.02 and 0.02. Given TAIEX’s highly volatility, my round trip duration of TXO is four days averagely.

Why my OI is four days. The reasons are below:

1. In the unpredictable stock market, the only predictable is the message changing, so timing is important for my opening my TXO interest and closing my TXO portfolio.

2. TXO is the fastest growing derivatives in the world.

3. TXO’s transaction tax is low and much cheaper than others.

4. TXO is quite liquid.

5. TXO premium is based on a multiplier of $NT 50 per index point. One point is $NT 50.

Investors differ systematically in their trading strategies.

Some have a tendency towards buy TXO, while others have a tendency towards sell TXO.

Some have a tendency towards TXO calls, while others investors have a tendency towards TXO put.

Some have a tendency towards optimism (buy call and sell put), while others have a tendency towards pessimism (sell call and buy put).

Some trade under the rule that TAIEX is significantly positively auto correlated (point estimate is around 0.15). Buying calls after the market has gone up previous month, and Buying puts after the market has gone down previous month. Chasing recent good index performance is to buy calls.

Some prefer to buy out-of-the-money options and open a new position in that option contract, since these options are cheaper, offer higher leverage and more likely lottery tickets.

For hedge reason, some foreign & domestic institutions prefer to buy & hold long-term/out-of-the-money index puts. While I prefer to sell out-of-the-money options and open a new position in that option contract, because that most out-of-the-money options settlement value will be 0 on expiration date finally, that is[pic]and[pic].

I do not have fixed tendency, but I generally sell TXO with 20 days to maturity.

Unlike most institutions buy puts & calls for hedging purposes, I only sell put and sell calls for speculation purposes.

Unlike most institutions buy and hold TXO, I only sell TXO for very short-term (4 days holding period) regardless of the bull/bear market condition. I never buy and hold TXO till maturity.

Unlike most institutions trade both Taiwan stock index futures (hereafter TX) and TXO, I only sell TXO. Since March 27, 2006 foreign institutions are allowed to sell TXO.

Unlike most institutions trade combination orders (including vertical spreads, horizontal spreads, straddles, strangles, conversions and reversals).) , I only sell single orders.

I hope my living records will be of interest to researchers, practitioners as well as policy-makers.

I hope my living records will benefit China. 2010.04.16, China Financial Futures Exchange announced the Shanghai and Shenzhen 300 stock index futures contracts (IF1005, IF1006, IF1009 and IF1012) on listed and those four contracts begin from the price of 3399 points.)

The rest of this paper is organized as follows. Section 2 describes methodology.

Section 3 describes my data and present summary statistics about my trades, my trading behavior, realized return and my disposition effect. Section 4 concludes this paper.

2. Methodology

2.1 return in option

Consider a round trip consisting of [pic] contracts of short position in an option sold at [pic](=[pic]) per contract ([pic]),and [pic] contracts of long position in the same option entered at [pic](=[pic]) per contract ([pic]), with the property that my dollar profit associated with a round trip is [pic] The corresponding rate of return is defined as [pic]

These expressions apply to the case when the options are held till maturity, taking the price [pic]or [pic]as the intrinsic value of the long or short option position at maturity.

2.2 Logistic Regress

When the independent variable is binary variable. For example, TAIEX will go up or down tomorrow.

Logistic regression (sometimes called the logistic model or logit model) is used for prediction of the probability of occurrence of an event by fitting data to a logistic curve. It uses several predictor variables that may be either numerical or categorical. For example, the probability that TAIEX will go up or down tomorrow might be predicted by X1= foreign institutions net long and short in TX, X2= domestic dealer institutions net long and short in TX, X3=investment trust sector net long and short in TX, X4= TAIFEX the top five traders net long and short in TX, X5= TAIFEX the top ten traders net long and short in TX, X6= the opening quotation about the committee buys the number of sheets/ the committee sells the number of sheets, X7= the opening quotation about the spread between TAIFEX and TAIEX, X8= U.S. stock market closing price of Taiwan morning, X9= net foreign institutions buying (selling) amount in the previous trading day, X10= The previous trading day volume of puts/calls (hereafter P/C) ratio, X11=The previous trading day open interest (hereafter OI) of P/C ratio, X12= E-Mini Dow Jones futures e-tray happening during the same period of Taiwan time, X13=contemporaneous Shanghai Stock Index, and X14=CBOE Volatility VIX.

Logistic regression analyzes binomially distributed data of the form

[pic]

where the numbers of Bernoulli trials [pic] are known and the probabilities of success [pic] are unknown. An example of this distribution is the fraction of seeds ([pic]) that germinate after [pic]are planted.

The model proposes for each trial [pic] there is a set of explanatory variables that might inform the final probability. These explanatory variables can be thought of as being in a 14 vector [pic] and the model then takes the form

[pic].

The logits, natural logs of the odds, of the unknown binomial probabilities are modeled as a linear function of the [pic].

[pic]

Note that a particular element of [pic] can be set to 1 for all [pic] to yield an intercept in the model. The unknown parameters [pic] are usually estimated by maximum likelihood using a method common to all generalized linear models.

The interpretation of the [pic] parameter estimates is as the additive effect on the log of the odds for a unit change in the [pic] explanatory variable. In the case of a dichotomous explanatory variable, for instance gender, [pic] is the estimate of the odds of having the outcome for, say, males compared with females.

The model has an equivalent formulation

[pic]

This functional form is commonly called a single-layer perceptron or single-layer artificial neural network. A single-layer neural network computes a continuous output instead of a step function. The derivative of pi with respect to X = x1...xk is computed from the general form:

[pic]

Where f(X) is an analytic function in X. With this choice, the single-layer network is identical to the logistic regression model.

Table 1 presents variable definitions and Logistic Regress Model analysis

3. Results

3.1 Data

TAIFEX use TAIEX to derivate TXO(also TX etc. ), which are modeled after the S&P 500 index options, these TXO are cash-settled with European-style exercise. The amount of available strike price is similar to the S&P 500 index options. Five delivery-months are available: the spot month, the next calendar month, and the quarter months (March, June, September, and December). The expiration day is the third Wednesday of the respective months.

The strike price interval is 100 index points in spot month and the next two calendar months, 200 index points in the quarter-months.

In Taiwan, these trading systems (TAIEX, TX and TXO) are 100% electronic fully automated. My dataset is provided by TAIFEX.

My transaction data include option characteristics (e.g., strike price, maturity, and call/put indicator), trade price, volume, date, time, buy/sell indicator, and whether the order opens a new option position or closes a previous established position.

3.2 Summary Statistics of Index Options in My Trades

Out-of-the-money put options are that strike (exercise) prices are lower than its underlying assets (TAIEX).

Contrarily, out-of-the-money call options are that TAIEX are lower than their strike prices.

Deep out-of-the-money put options have strike prices that are between 93% and 98% of the contemporaneous index level, and deep out-of-the-money call options have strike prices that are between 102% and 107% of the contemporaneous index level. Deep out-of-the-money put (call) options have strike prices at least 7% below (below) the index level. Other options are classified as near- and in-the money options.

Table 2 presents　Trading Strategy and Performance.

3.3 Summary Statistics of My Trades: Empirical Results

The basic unit of our trading performance analysis is one complete round trip of trades, which is a series of offsetting open and close trades. A round trip starts when an investor establishes a new position in an option contract, and terminates when the position either expires or is closed by offsetting positions (There is no early exercise since the TXO is European style).

Table 3 reports my data from 2010/05/23 to 2010/11/30. My OI is concentrated on short-term options, and has a tendency towards index puts. I first compute the profits and realized returns of each round trip of my trades. The aggregate of my profits/loss is $NT 461,445. The realized profits/loss is based on the actual transaction prices which account for the commissions, tax and the bid-ask spreads.

3.4 Disposition Effect

Numerous studies show that investors are affected by the disposition effect--they tend to sell winners too soon but hold on to losing positions for too long (e.g., Shefrin and Statman 1985, Odean 1998).

I measure a tendency to display my disposition effect by comparing the average duration of my round trips with negative returns [pic] to the average duration of my round trips with positive returns [pic]. Investors with higher value of [pic] are more subject to the disposition effect.

I hold the winning trades longer time than the losing positions by 1.5 times averagely. I do not have the disposition effect in my trades.

4. Conclusions

Option studies have predominately focused on no-arbitrage valuation. However, little is known about investors' trading behavior and actual realized return. This paper contributes to the literature by providing a detailed analysis of my trading behavior and performance in the TXO market using my complete trading record.

My record tell you

1) My trading strategy is simple but not easy. Selling and hold out-of-the-money TXO is simple but obeying this rule is not easy.

2) I prefer to start to sell and open a new position regardless of market condition, the moneyness and maturity. In my OI, I most often have net short position in puts & calls with out-of-the-money.

3) In my OI, I most often have a position with maturity under 20 days.

4) My OI period is 4 days averagely.

5) TXO held for short periods and sold prior to expiry exhibit average returns which confirm to theory as per Branger, Nicole, Alexandra Hansis, and Christian Schlag (2009).

6) The average realized returns for long index call positions are significantly lower than the short index call positions which confirm to theory as per Ni, Sophie (2008).

l.

References

1) Branger, Nicole, Alexandra Hansis, and Christian Schlag, 2009, Expected option returns and the structure of jump risk premium, Working Paper, University of Munster and Goethe University.

2) Ni, Sophie, 2008, Stock option returns: A puzzle, Working Paper, University of Illinois, Urbana-Champaign.

3) Tannous, George, and Clifton Lee-Sing, 2008, Expected time value decay of options: Implications for put-rolling strategies, vol. 43, pp. 191--218.

4) Are broad market shocks anticipated by investors? Evidence from major equity and index options markets , Working Paper, Athens University.

5) Chao-Hui Yeh 2006 " The Study on Expiration Day Effect of TAIFEX," Taiwan's futures and derivatives journal, vol. 4, pp. 72 – 94.

|Table 1 presents variable definitions and Logistic Regress Model analysis |

|If p>0.9, then buy calls. |

|If 0.9>p>0.75, then sell puts. |

|If p ................
................

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