Return calculations

One important aspect of our methodology involves the choice of time regime used to perform the return calculations. Financial theory has presented us with two possibilities, the event and calendar time approach. The event time approach consists in calculating returns in a time regime that is relative to the entities’ issuance date. A considerable amount of studies have preferred the use of event time approach. However, Brav Gompers (1997) and Gomper and Lerner (2003) have shown evidence of a cross-sectional dependence between IPO stocks when using the event time approach. Schöber (2008) Contends that a cross-sectional dependence can influence the results of return calculations overestimating the t-statistics in an event time regime. The calendar time approach on the other hand is able to correct the cross-sectional dependence by tracking the performance of a portfolio in calendar time. Fama (1998) contends that the calendar time approach is superior to the event regime in that it controls for heteroskedasticity and gives more weight to calendar months preceding high IPO activity. Since the distribution of IPO issuances

across our time horizon fluctuates due to hot IPO periods we have decided to follow the calendar time approach per Fama (1998) and Schöber (2008).

6.2.2.1 Cumulative Abnormal Return

The Buy and Hold Abnormal Return (BHAR) and the Cumulative Abnormal Returns (CAR) are the two most commonly used methodologies to calculate abnormal stock returns. The BHAR is said to be the difference between the IPO sample and the benchmark compounded monthly over the time horizon. Draho (2004) argues that one of the advantages of the BHAR is that it incorporates compounding emulating better the investor’s experience. However, he acknowledges that compounding creates statistical problems such as extreme skewness and inflated abnormal returns. While he argues that these same problems could affect the CAR he recognizes that the extent to which results are affected is considerably less. Additionally, the time required to adjust abnormal returns is likely to be overstated Fama (1998). The CAR on the other hand, while calculating the returns similarly to the BHAR, differs in that it accumulates the excess returns throughout the time horizon. Fama (1998) argues that the strengths of the CAR model are threefold. Asset pricing models assume normally distributed returns, returns are normalized better on a monthly basis rather than yearly and prices adjust sooner after abnormal returns. We deem the CAR as the better of the two methodologies and the cumulative abnormal returns are measured by the given formula:

∑

∑

Where, and represents return on the entities and a benchmark portfolio respectively. The abnormal return is accumulated in accordance to the entities classification resulting in , and . We elaborate on the weights of the abnormal returns on section 6.3.3.1. Note that in calendar time measurements, the accumulation and weighting of portfolios’ returns are calculated in actual trading dates.

6.2.2.2 Single Factor Regression - Capital Asset Pricing Model

Draho (2004) suggests that one of the strongest advantages of the asset pricing model is that it offers the possibility of constraining and identifying anomalies in the cross section analysis.

Moreover, asset pricing models allow researchers to build simple statistics around the model to test for abnormal return hypothesis. The asset pricing approach is based on risk pricing theoretical background and has three main models; capital asset pricing model (CAPM), Fama-French three factor model and the arbitrage pricing theory (APT). In this paper however we focus exclusively on the first two as we have found them predominant in financial literature.

The CAPM is founded on the premise that the only relevant risk factor for a firm is its market return. The model states that the expected return for stock equals the risk-free interest rate plus stock’s beta times the Market Risk Premium Merton (1987). The stock’s abnormal return is calculated as the difference between the post-IPO realized return in excess of the free risk rate and the net expected return. Hence, when regressing the net realized return on excess of the market risk premium we can measure underperformance through the intercept, alpha . The formula is as following, where represents the return on the sample portfolio, , the estimated Nordic Risk Free Rate and the return on benchmark index.

( ) 6.2.2.3 Three Factor Regression – Fama-French

Fama and French (1993) tested stock returns using a three factor model that is similar to the CAPM, but it includes two additional factors to the equation. As opposed to CAPM, the Fama and French model is not an equilibrium relationship and it controls for the size and value effects on returns.

( )

As with the Single Factor Regression – CAPM, represents the return on the sample portfolio, is the estimated Nordic Risk Free Rate and is the return on benchmark index. The

additional factors controlling for the size and value effects are the Small Minus Big (SMB) and High Minus Low (HML).

Fama and French had developed a methodology to build the benchmark portfolios using two different types of sorting; size and value. In latter versions, size breakpoints are determined by the median of the NYSE market equity, while the book-to-market is given by the 30^th and 70^th NYSE percentiles. However, as of 2012 and per their paper “Size, Value, and Momentum in International Sock Returns” Fama and French offer a new sorting methodology for size that find the breakpoints at the top 90% and the bottom 10% of the market cap respectively. Per Fama (1997) the size factor or SMB is the equally weighted average of the returns on three small stock portfolios for the region in excess of the average of the returns on three big stock portfolios. The HML factor is calculated as the equally weighted average of the returns of the two high book-to-market portfolios for a region minus the average of the returns for the two low book-to-book-to-market portfolios. The factors are estimated from the ad-hoc Nordic Index.

6.3 The Variables