Sample Distribution and Summary Statistics

Table 3.2 shows the time series distribution of secured debt ratio, CEO option portfolio sensitivities to stock price (LNDELTA-delta in logs) and CEO option portfolio sensitivities to stock return volatility (LNVEGA-vega in logs) and leverage.

For the right skewness of the distributions of vega and delta, natural logarithm transformations are used in the empirical tests. The sample contains 360 observations and covers the periods from 2001 to 2009. All variables are defined in Appendix A.

There is an upward trend in the use of secured debt from 2001 until 2005, followed by

a general decline, then reach the highest median value of 52% in 2009. Secured debt ratio obtains its lowest median value of 38% in 2001. Similarly the average sensitivity of CEO option portfolio to 1% change in stock return volatility (LNVEGA) rises from 2.469 in 2001 to the high value of 3.138 in 2005, and later reaches the peak at 3.242 in 2009 as secured debt ratio. As described in our hypothesis development section, an increase in vega increases CEO risk appetite, which possibly induce the increase in secured debt ratio (See “Free cash flow hypothesis” and “Cost contracting hypothesis”). Here coincidentally I find that secured debt ratio increases or decreases with vega. On the contrary, the fluctuations of LNDELTA and leverage have not exhibited the same trend over my sample period.

Table 3.2 Sample Distribution

This table shows the time series distribution for the sample. In each year, the number of REITs is in column two. The average secured debt ratio of all REITs in given year is shown in column three. In the following columns, I exhibit the mean value of LNVEGA, LNDELTA and leverage across firms in each year. The sample contains 360 observations and covers the periods from 2001 to 2009. All variables are defined in Appendix A.

Year Number

of REITs

SECURED

DEBT RATIO LNVEGA LNDELTA LEVERAGE

2001 16 0.380 2.469 4.099 0.363

variables in the regressions. The first dependent variable secured debt ratio has a mean value of 46.2%, and the second dependent variable, excess return, has a mean value of -0.0001. Turning to the treatment variables, again, natural logarithm transformations are used in the empirical tests due to the right-skewed distributions of vega and delta. LNDELAT has a median of 4.4290 and LNVEGA has a median of 3.0270. The statistics for both treatment variables are similar to Coles et al. (2006).

They compute the medians of delta and vega are 206 and 34 in absolute value, taking natural logarithm, the medians of LNDELAT and LNVEGA are around 5.3279 and 3.5264 respectively. In Table 3.3B, detailed statistics for delta and vega decomposition are provided to make a better understanding of original delta and vega.

Table 3.3A Summary Statistics

This table shows the summary statistics for all dependent and independent variables in the regressions. The sample includes 360 observations and covers the period from 2001 to 2009.

All variables are defined in Appendix A.

CASHCOMP_RATIO 0.4237 0.2062 0.3726 0.6145 0.2725 360

Table 3.3B Descriptive Statistics of DELTA and VEGA Decomposition

This table shows the descriptive statistics for delta and vega decomposition in original form (before natural logarithm transformation). P denotes option portfolio. NG, PGEX, PGUN and STOCK stand for new grants, previously granted exercisable options, previously granted unexercisable options, and CEO stock holdings, respectively. The sample includes 360 observations and covers the period from 2001 to 2009.

Variable($000) Mean 1st Quartile Median 3rd Quartile Std.Dev N DELTANG 23.7528 5.4102 14.0547 26.0239 31.1743 360 DELTAEX 57.9458 4.9626 24.9978 84.3580 76.5963 360 DELTAUN 228.7001 34.9142 76.4735 159.6129 503.1428 360 DELTASTOCK 810.8894 32.1204 121.8691 384.5137 3470.4290 360 DELTAp 816.9410 32.1204 163.2888 446.9397 3253.8560 360

VEGANG 1.3400 1.1530 1.3080 1.4870 0.2750 360

VEGAEX 0.3619 0.2892 0.3616 0.4347 0.1356 360

VEGAUN 35.9587 10.4499 21.6622 43.6445 43.9927 360

VEGASTOCK 91.9160 4.0898 41.9231 131.6555 128.0958 360

VEGAP 151.9873 26.3124 65.0565 108.8831 292.5760 360

In Table 3.4, I examine the correlation among secured debt ratio, LNDELTA, LNVEGA and other firm characteristics. It is shown that LNDELTA and LNVEGA are significantly correlated with coefficient of 0.7736. Thus, it is crucial to control LNDELTA when I consider the effect of LNVEGA on the dependent variables.

Table 3.4 Correlation between Secured Debt Ratio, LNDELAT, LNVEGA and Firm Characteristics

This table shows the correlation between managerial incentives (LNVEGA, LNDELTA) and firm characteristics. The sample contains 360 observations from 2001 to 2009. All variables are defined in Appendix A. ***, **, and * are used to indicate that the coefficient is significantly different from zero at the 1%, 5%, or 10% level, respectively.

SECURED

Figure 3.1 displays the scatter plot of average firm secured debt ratios and within firm standard deviations of secured debt ratios. The idea behind this presentation is to see if variations in secured debt ratios are common or if firms rarely adjust secured debbt ratio. It is clear from Figure 3.1 that few firms target particular secured debt ratios and do not change their ratios (note the low volatilities around 0% and 100%).

However, this figure reveals that many REITs do have wide variations in secured debt ratios over the sample. Figure 3.1 provides sufficient variability that makes the analysis of secured debt ratio meaningful.

Figure 3.1 Scatter Plot of Within Firm Secured Debt Ratio and Secured Debt Ratio Volatility

To have a better understanding of the distributions of LNDELTA and LNVEGA, Fig 3.2 and Fig 3.3 are provided. Fig 3.3 and Table 3.3 seem to indicate that LNVEGA of REITs has relatively larger mean and variance compared with other sectors. In Brockman et. al (2010), the sample includes industrial firms with SIC codes from 2000 to 5999, which excludes REITs (SIC code: 6798). According to their statistic description, mean of LNVEGA is 1.108, variance is 1.913.Also 25 percentile, median and 75 percentile are all smaller than those in Table 3.3. Similar result can be obtained when I compare LNVEGA of this work with others (Chava & Purnanandam, 2010;

Coles et. al, 2006). This result might suggest that REITs has larger LNVEGA than other sectors. Since LNVEGA represents managerial risk-taking incentive, higher LNVEGA means that REITs might have higher managerial risk-taking incentives than other sectors. So it could provide a good motive for examining REIT equity

Scatter Slot of within Firm Secured Debt Ratio and Volatility of Secured Debt Ratio

compensation and risk-taking incentive when other works exclude REITs in their samples.

Figure 3.2 Scatter Plot of Within Firm LNDELTA Mean and Standard Deviation

Figure 3.3 Scatter Plot of Within Firm LNVEGA Mean and Standard Deviation

0

Scatter Slot of within Firm LNDELTA Mean and Standard Deviation

Scatter Slot of within Firm LNVEGA Mean and Standard Deviation

Mean value of LNVEGA sorted by firm StandardDeviation of LNVEGA sorted byfirm

3.5 Summary

This chapter introduces data sources and sample selection, variable descriptions and summary statistics. More importantly, this chapter descries the detailed calculation processes of key independent and dependent variables. Through the careful examination of variables, the key variable, LNVEGA of REITs is found to have higher value and higher variance than other sectors, which make the test of REIT managerial risk-taking incentive through LNVEGA more different and interesting. In order to obtain a comprehensive understanding of the influence of compensation incentives on secured debt, careful empirical design and result interpretations will be followed in the next chapter.