Data, Risk Factor Construction and Methodology

I have seen, from Chapters 3 and 4, that the uniqueness of Hong Kong’s regulations on short- sales provides an ideal laboratory for exploring the differences in stock pricing behaviour and in the performances of asset-pricing models, the differences being due to two opposite short- selling statuses. In fact, the designated short-selling list also enables me to construct the no- shorting risk factor. According to the designated short-selling list, at any point in time, a stock stays either on the list, or off the list. I can, therefore, differentiate individual stocks’ short-selling statuses: If a stock is on the list, I refer to it as “shortable”; if a stock is off the list, I refer to it as “non-shortable”. The detailed description of the Hong Kong designated short-selling list has already been given in Chapter 2. This chapter adopts the same sample period of addition/deletion stocks in the Hong Kong stock market as in Chapter 4. The changes of the designated short-selling list are provided by Table 2.1 in Chapter 2.

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To construct risk factors33 and form portfolios, I collect the following data for each individual stock traded on the HKSE; closing prices, market value (ME), book value (BE), and the number of shares outstanding. I also obtain the monthly Hong Kong 3-month Treasury bill rate (T-bill) as a proxy for the risk-free rate. All of the above data come from the Datastream database.

In constructing the size and book-to-market risk factors, I follow Fama and French (1992, 1993). Specifically, I sort all the stocks listed on the HKSE at the end of June of each year t based on their market value (ME) and classify them into the two size groups: Stocks with ME above (below) the cross-sectional median are classified as big (small) stocks and denoted as B (S). Meanwhile, I rank all the stocks based on their book-to-market ratios (BM) and classify them into one of the three BM groups: Stocks with the highest (lowest) 33% BM are classified as high (low) book-to-market stocks and denoted as H (L), with the remaining 33% classified as medium book-to-market stocks and denoted as M. These independent 2u3 sorts allow me to construct six size and book-to-market portfolios (S/L, S/M, S/H, B/L, B/M and B/H) from the intersections of the two size and the three book-to-market groups. For example, the S/L portfolio contains the stocks in the small-size group that are also in the low book-to-market group, and the B/H portfolio contains the big-size stocks that also have high book-to-market ratios. I calculate monthly value-weighted returns on the six portfolios from July of year t to June of year t+1, and reform the portfolios at June of each year. To be included in the test, a firm must have closing prices for December of year t-1 and June of year t, and book equity for year t-1.

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Risk factors for the Hong Kong stock market are not available from the Data Library website of Professor Kenneth French. So, I construct all of them, adopting the approach proposed by Fama and French (1992, 1993, 1996).

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Below are the details34 of each risk factor to be used in this study. The size factor is represented by the portfolio returns denoted as SMB (small minus big), meant to mimick the risk factor in returns related to size. The SMB returns are calculated as the difference, each month, between the simple average of the returns on the three small-stock portfolios (S/L, S/M, and S/H) and the simple average of the returns on the three big-stock portfolios (B/L, B/M, and B/H):

3

S L B L S M B M S H B H

SMB

In short, SMB is the difference between returns on small-stock portfolios and returns on big- stock portfolios. This difference is largely free of the influence of BE/ME, focusing instead on the different return behaviours of small and big stocks.

The BE/ME factor is represented by the portfolio returns denoted as HML (high minus low), meant to mimick the risk factor in returns related to book-to-market equity. The HML returns are calculated as the difference, each month, between the simple average of the returns on the two high-BE/ME portfolios (S/H and B/H) and the simple average of the returns on the two low-BE/ME (S/L and B/L) portfolios:

2

S H S L B H B L

HML

HML is largely free of the size effect in returns, and focuses on the different return behaviours of high-BE/ME and low-BE/ME stocks.

34 _{The constructions of the market, size and book-to-market factors are the same as in Chapter 4, however, in}

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True mimicking portfolios for the common risk factors in returns will minimise the variance of firm-specific factors. The six size-BE/ME portfolios in SMB and HML are value- weighted, to be in the spirit of minimising variance and reducing estimation bias35. More importantly, use of value-weighted components results in mimicking portfolios that capture the different return behaviours of small and big stocks, or high-BE/ME and low-BE/ME stocks, in a way that corresponds to realistic investment opportunities.

I proxy the market factor by excess market returns denoted as RM-RF. RM is the returns on the value-weighted portfolio of the all shares in the Hong Kong market, and RF is the Hong Kong 3-month Treasury bill rates (T-bill).

I use two alternative measures for the momentum factor WML; The Carhart momentum factor MOM_CARH, and the Fama-French momentum factor MOM_FF. MOM_CARH represents the portfolio returns constructed following Carhart (1997). The winner (loser) portfolio W (L) consists of firms with the top (bottom) 33% returns in the past 11 months prior to month t-1, and the momentum factor is simply the difference between equally-weighted portfolio returns of W and those of L:

MOM_CARH = Winner_PROTFOLIO – Loser_PORTFOLIO

I construct the Fama-French momentum factor (available on Kenneth French’s website for many stock markets, but not for Hong Kong) in the following way: It uses the intersections of two value-weighted size portfolios and three value-weighted portfolios formed on prior returns (all Hong Kong stock returns in the past eleven months prior to month t-1). This momentum factor is the simple difference between the average return on the

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Asparouhova, Bessembinder and Kalcheva (2012) point out that equally-weighted returns of portfolios constructed based on firm characteristics could produce estimation bias.

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two top prior return portfolios and the average return on the two bottom prior return portfolios:

_

2

S Top S Bottom B Top B Bottom

MOM FF

The no-shorting factor NMS is the difference in returns between the portfolio of non- shortable stocks and the portfolio of shortable stocks, meant to mimick the risk factor related to short-sale constraints. The factor is constructed as follows. Using the same rebalancing scheme as for the 25 size/BM portfolios, SMB and HML, I sort all stocks based on whether or not they are on the shorting list at the end of June of each year t, and classify them into each of the two portfolios; shortable, and non-shortable. I then hold the two portfolios for 12 months (as I do for size/BM, SMB and HML portfolios), and calculate their respective monthly value-weighted returns. The shorting factor is then equal to non-shortable portfolio returns less shortable portfolios returns, and is denoted as NMS12. The constituent stocks in the shortable, the non-shortable and, hence the NMS12 portfolio, do not change between the end of June of year t and the end of June of year t+1. For comparison purposes, I also consider the 1-month holding period for the no-shorting factor portfolio, which is denoted as NMS1. Specifically, in each month, I classify all stocks into shortable and non-shortable portfolios, according to whether or not they are on the short-selling list in that month, and calculate their respective monthly value-weighted returns. NMS1 is then equal to the difference between the two portfolios’ returns, so the constituent stocks in the two portfolios and, hence, in NMS1 may change from month to month. Since the rebalancing period of NMS1 is different from, while NMS12 has the same rebalancing period as, that for the

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size/BM portfolios, SMB and HML, I will discuss the results involving NMS12 in the main text, while leaving the results involving NMS1 to the appendix of this chapter.

To examine the explanatory power of the no-shorting risk factor for variation in stock returns, I employ the Fama-Macbeth (Fama & MacBeth, 1973) two-pass regression method. The first pass runs the time-series regressions, as Fama and French (1992, 1993) do. By regressing each of 25 size-B/M portfolio returns on five common factors (including the no- shorting factor NMS) over the sample period, I can obtain direct evidence of whether NMS causes the 25 portfolio returns to vary together, in addition to their variations explained by the other four factors. The regression model is:

Rpt - Rft = Dp + Ep(Rmt - Rft) + spSMBt + hpHMLt + mpMOMt + npNMSt + Hpt (5.1)

where the dependent variables Rpt - Rft are excess returns on 25 size-B/M portfolios (i.e., p =1,

2,…, 25), formed on size and the book-to-market ratio of stocks36; Rmt - Rft are the excess

returns on the market portfolio; SMBt is the size factor; HMLt is the value (book-to-market)

factor; MOMt is either the Carhart momentum factor (MOM_CARTH), or the Fama-French

momentum factor (MOM_FF); and NMSt is the no-shorting factor. Dp is the intercept

measuring abnormal returns. Ep, sp, hp, mp and np are the slope coefficients, which measure

the sensitivity of the return on portfolio p to their respectively associated factors. If NMSt is a

risk factor and helps explain stock returns, I expect its loading np to be statistically significant,

and the adjusted R2 to be higher than if NMSt was not included in Equation (5.1). As in

Chapter 4, I employ conventional statistics (such as the adjusted R2 and the GRS F) to compare the performances of the FF three-factor model, the FF four-factor model (with

36 _{In Chapter 4, I form 25 size-B/M portfolios respectively for shortable and non-shortable stocks. In this chapter,}

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MOM_FF added), the Carhart four-factor model (with MOM_CARTH included) and my five-factor model with the no-shorting factor added.

The second pass runs cross-sectional regressions, through which I examine how well the average premiums for the five proxy risk factors explain the cross-section of average returns on stocks.