The following multivariate linear regression model for the verification of the benefits of diversification was estimated using the returns of the 28 CFO structures identified in the previous section.
CFOj,hk,t =δj,hk,t +β1j,hk STOCKt +β2j,hk DEFt +β3j,hk LIQt +β4j,hk TERMt +β5j,hk TRENDt +εj,hk (9) where:
δj,hk,t is the constant term for the CFOj, subjected to the set of preference Eh and the
diversification constraint k, at time t;
CFOj,hk,t is the monthly return of CFOj, constructed using the hedge fund portfolio subjected to the set of preference Eh and the diversification constraint k, at time t.
STOCKt is the monthly return of the Russel 3000 stock index at time t. It is used as an indicator of financial market performance and is included so as to determine whether systematic exposure to equity returns has an explicative power with regard to the performance of a securitized hedge fund portfolio.
DEFt is the spread in basis points of the LUCI Total OAS6 index at time t and is used as an indicator of the systematic default risk of credit markets. It is included in the model so as to ascertain whether systematic default risk in the credit markets influences CFO returns. To this end, several variables are used in the literature to capture this notion of default. However, as stipulated in Longstaff, Mithal and Neis (2005), among others, since the advent of the Credit Default Swaps (CDS) market, it has become common practice to use the spreads on these instruments to identify the default risk embedded in credit risk7.
LIQt is the spread in basis points between 10-year on-the-run and off-the-run government securities at time t. The variable is used as an indicator of the systematic liquidity risk of bond markets. This indicator is further explained in Longstaff, Mithal and Neis (2005).
TERMt is the spread in basis points between long-term (20-year) and short-term (1-month t-bills) government securities at time t. It is used as an indicator of systematic interest rate risk. This indicator is the same as that used in Fama and French (1993).
6 LUCI is the acronym for Liquid US Corporate Indices, a series of bond indexes developed by Crédit Suisse. The Total OAS (Option Adjusted Spread) version captures the entire market, eliminating the specific nature of securities such as embedded options.
7 The original intention was to use the CDX.NA.IG index spread. However, a thorough study of the series shows that there is a lack of liquidity prior to 2004, which could bias the results.
TRENDt is the typical time trend that is used when the variables are distributed over time. The idea is to eliminate any time trend effect that may result in autocorrelation in the data series.
Table 9 presents the value of the estimated coefficients and their respective p-value. We recall that the ideal scenario is that of completely uncorrelated returns, i.e. statistically null coefficients. In the case of the constant δj,hk,t its statistical significance implies the presence of a fixed effect not captured by the model’s variables.
<Table 9>
We first note that the constant δj,hk,t and the coefficient β5, which is attributed to the TREND variable, are always significant. This means, on the one hand, that returns are specific to each of the instruments. In addition, we see that the values taken by δj,hk,t are always positive and increase as leverage increases, thus reflecting greater added-value.
On the other hand, the significance of β5 confirms that there is indeed a trend in terms of CFO returns. It is also interesting to note that this coefficient is always negative, implying that returns decrease over the period studied (2001-2008).
When we consider the estimated coefficients of the variables of interest, β1 to β4, it is important to emphasize at the very outset that the statistical significance of the coefficients follows a rather consistent pattern across the different CFO structures tested. Indeed, the same pattern in terms of the statistical significance of the regression coefficients is exhibited in the case of direct exposure to the portfolio of hedge fund and CFO 11, whereas CFOs 15 and 18 present fewer significant coefficients. It can therefore be inferred that leverage has very little effect on systematic diversification. The benefits of diversification are therefore not an argument in favor of CFOs.
Regardless of the choice of underlying portfolio and of the selected capital structure, the coefficient estimates indicate that the liquidity (LIQ) and slope of the term structure (TERM) variables do not significantly impact CFO returns. With respect to the STOCK variable, which relates to systematic equity market risk, we note that the estimated
coefficient is almost always significant. The estimated coefficient for the default risk variable is less stable across the different CFO structures. In the case of exposure to CFO 1 and CFO 11, we see that the DEF variable has a significant, negative impact in the case of underlying portfolios E1;100%, E2;20% and E5;15%. For CFOs 15 and 18, there is a gradual loss of significance of the estimated coefficient for the last two underlying portfolios (E2;20% et E5;15%).
Thus, it is the unconstrained mean-variance portfolio that fairs the most poorly in terms of systematic risk exposures, while the unconstrained version of preference set E2
demonstrates the least dependence to the selected systematic risk factors. We recall however that this underlying portfolio underperforms in terms of most performance measures. It therefore appears necessary to reach a compromise between performance and decorrelation with the capital market as the best of both worlds can not be achieved simultaneously. Two interesting alternatives appear to be that of E4;10% and the equally-weighted portfolio that both exhibit a slight positive correlation with equity markets.
Although not an optimal solution, these results provide strong evidence that it is possible to construct CFOs that generate value in terms of both performance and low systematic risk exposure.
On the basis of the results above, when the objective pursued by the investor in terms of CFO equity is either performance, or decorrelation, an unconstrained portfolio in which Foreign Exchange strategy is predominant is essential. Where one wishes to combine the two objectives, there must be substantial diversification of the underlying portfolio.
With regard to the debt-to-equity ratio of the capital structure selected, there is almost no impact, notwithstanding exceptions. This therefore implies that CFOs represent added-value compared to a direct exposure to the portfolio of hedge funds, only in terms of performance however, not with regard to diversification in capital markets.
5. CONCLUSION
In response to suggestions that CFO Equity Tranches do not offer value to investors, we decided to undertake a thorough examination of the performance of this type of investment. The objective was to assess the performance of the Equity Tranche of CFOs both in terms of risk-adjusted return as well as systematic risk exposures. For this purpose, 30 optimal portfolios (each conditional to a set of preferences and weight constraints) and an equally-weighted portfolio were constructed using 16 hedge fund strategy indexes. All of these underlying portfolios were then securitized using 19 capital structures, which allowed us to analyze the series of returns of 620 CFO Equity Tranches.
Interestingly, we observe that if we consider the overall distribution of returns of a CFO Equity Tranche in analyzing the performance, securitizing and tranching the underlying portfolio of hedge funds adds value for the end investor. Our analysis also finds that there was no direct relationship between the optimal portfolio to securitize and the capital structure decisions. With regard to the debt-to-equity ratio, we conclude that leverage is beneficial for the CFO equity holder when the level of debt is maximized for a given funding cost. In addition, our analysis shows that a trade-off takes place between performance and systematic diversification; if one considers a combination of the two objectives, we conclude that the underlying portfolio must be broadly diversified across the various hedge fund strategies. Thus, these conclusions suggest that market participants might have been too hasty in dismissing CFOs, and not taking greater advantage of the benefits offered by these investment vehicles.
If the reputation of securitization had not already been undermined by its involvement in the current financial crisis, the impact of this two-dimensional analysis could have been rather different. However, given the present stigma attached to structured products, we should not expect to witness new CFO transactions anytime soon. This is unfortunate considering that the nature of the problem is one of inaccurate valuation rather than one of overexuberant financial engineering, as explained in Longstaff and Myers (2009).
Global financial markets are currently seeking to rebuild a sound financial system and it will be interesting to see whether CFOs will be favored among the range of investments available to institutional investors. For this to transpire, securitization and financing practices must be rehabilitated in conjunction with proper governance rules that promote greater transparency.
Since it is only a matter of time before financial markets have had the chance to digest the consequences of the current crisis, it is relevant to pursue this research further.
Under this new analysis, it would be consistent to consider alternative ways in which to further expand on the conclusions. For example, an actively-managed underlying portfolio could be of interest. Indeed, rather than turning to strategy indexes that are not readily investible, it would be suitable to use investments in specific funds and make readjustments as necessary. From a risk management viewpoint, it would be appropriate to examine the potential tools that would allow exposure to a CFO Equity Tranche to provide strong risk-adjusted performance with negligible exposure to systematic risk factors. Finally, it would be important to assess the impact of high market stress (like the one that prevailed in 2007 and 2008) in order to analyze the behavior of CFOs in such circumstances.
REFERENCES
Amin, G. S., and H. M. Kat. “Hedge Fund Performance 1990-2000: Do the Money Machines Really Add Value?”, Journal of Financial and Quantitative Analysis, (2003), 38(2):251-275.
Amin, G. S., and H. M. Kat. “Stocks, Bonds and Hedge Funds: Not a Free Lunch!”, Working paper, ICMA Centre, University of Reading, Berkshire (2002).
Boakye, C. “Multidimensional Risk/Performance Measurement for Hedge Funds.”, Working paper, Temple University’s MSFE program, Philadelphia (2008).
Cheng, C. “Securitization & Hedge Funds: Creating a More Efficient Market.”, Working paper, Intangis, Renaissance Capital Group, New York (2002).
Chunhachinda, P.; K. Dandapani; S. Hamid; and A. Prakash. “Portfolio Selection and Skewness:
Evidence from International Stock Markets.”, Journal of Banking and Finance, 21 (1997), 143–
167.
Davies, R. J.; H. M. Kat; and S. Lu. “Fund of Hedge Funds Portfolio Selection: A Multiple-Objective approach.”, Journal of Derivatives and Hedge Funds, Forthcoming (2009).
DeMiguel, A-V.; L. Garlappi; and R. Uppal. “How Inefficient are Simple Asset-Allocation Strategies?”, Working paper, London Business School, Centre for Economic Policy Research, London (2005).
De Souza, C., and S. Gokcan. “Allocation Methodologies and Customizing Hedge-Fund Multi-Manager Multi-Strategy Products.”, Journal of Alternative Investments, 6 (2004), 7-21.
Fama, E., and K. French. “Common Risk Factors in the Returns on Stocks and Bonds.”, Journal of Financial Economics, 33 (1993), 3-56.
Fung, W., and D. A. Hsieh. “Asset Based Style Factors for Hedge Funds.”, Financial Analysts Journal, 58 (2002), 16-27.
Genest, C., and B. Rémillard (2004). “Tests of Independence and Randomness Based on the Empirical Copula Process.”, Test, Sociedad de Estadistica e Investigacion Operativa, 13 (2004), 335-369.
Gregoriou, G. N., and J-P. Gueyie. “Risk-Adjusted Performance of Funds of Hedge Funds using a Modified Sharpe Ratio.”, Journal of Wealth Management, 6 (2003), 77-83.
Jarque, C. M., and A. K. Bera. “Efficient Tests for Normality, Homoscedasticity and Serial Independence of Regression Residuals.”, Economic Letters, 6 (1980), 255-259.
Keating, C., and W. F. Shadwick. “A Universal Performance Measure.”, Working paper, The Finance Development Centre, London (2002).
Lilliefors, H. W. “On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown.”, Journal of the American Statistical Association, 62 (1967), 399-402.
Lee, S. L. “Modified VAR and the Allocation to Real Estate in the Mixed-Asset Portfolio.”, International Real Estate Business School, University of Regensburg, Regensburg (2007)
Longstaff, F. A.; S. Mithal; and E. Neis. “Corporate Yield Spreads: Default Risk or Liquidity? - New Evidence from the Credit-Default Swap Market.”, Journal of Finance, 60 (2005), 2214-2254.
Longstaff, F. A., and B. Myers. “Valuing Toxic Assets: An Analysis of CDO Equity.”, Working paper, NBER (2009).
Mahadevan, S., and D. Schwartz. “Hedge Fund Collateralized Fund Obligations.” Journal of Alternative Investments, 5 (2002), 45-62.
Missinhoun, J., and L. Chacowry. “Collateralized Fund Obligations: The Value of Investing in the Equity Tranche.”, Journal of Structured Finance, 10 (2005), 32-37.
Sharpe, W. F. “Mutual Fund Performance.”, Journal of Business, 39 (1966), 119-138.
Sortino, F. A., and L. N. Price. “Performance Measurement in a Downside Risk Framework.”, Journal of Investing, 3 (1994), 59-65.
Stone, C. A., and A. Zissu. “Fund of Fund Securitizations.”, Journal of Derivatives, 11 (2004), 62-69.
Sun, Q., and Y. Yan. “Skewness Persistence with Optimal Portfolio Selection.”, Journal of Banking and Finance, 27 (2003), 1111–1121.
Tayi, G., and P. Leonard. “Bank Balance Sheet Management: An Alternative Multiobjective Model.” Journal of Operations Research Society, 39 (1988), 401–410.
Treynor, J. L. “How to Rate Management of Investment Funds.”, Harvard Business Review, 43 (1965), 63-75.
Table 1 Structural Assumptions for the 20 CFOs Considered ts the 20 capital structures considered. The characteristics of each structure appear on the vertical axis, while the 20 CFO structures are presented horizontall n of the table shows the features of the five possible tranches and the lower one relates to cost assumptions. Shaded areas designate the absence of a certain tranc CFO 1CFO 2CFO 3CFO 4CFO 5CFO 6CFO 7CFO 8CFO 9CFO 10CFO 11CFO 12CFO 13CFO 14CFO 15CFO 16CFO 17CFO 18CFO 19 s AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA $20 M$40 M$60 M$80 M$100 M$120 M$140 M$160 M$180 M$200 M$200 M$200 M$200 M$200 M$200 M$200 M$200 M$200 M 5%10%15%20%25%30%35%40%45%50%50%50%50%50%50%50%50%50% 60%60%60%60%60%60%60%60%60%60%60%60%60%60%60%60%60%60% BBBBBBBBBBBBBBBBBBBBBBBB $20 M$40 M$60 M$80 M$80 M$80 M$80 M$80 M 5%10%15%20%20%20%20%20% 75%75%75%75%75%75%75%75% BBBBBBBB $20 M$40 M$60 M$60 M 5%10%15%15% 82%82%82%82% BB- $20 M 5% 90% - $ $20 M$40 M$60 M$80 M$100 M$120 M$140 M$160 M$180 M$200 M$220 M$240 M$260 M$280 M$300 M$320 M$340 M$360 M $400 M$380 M$360 M$340 M$320 M$300 M$280 M$260 M$240 M$220 M$200 M$180 M$160 M$140 M$120 M$100 M$80 M$60 M$40 M 100%95%90%85%80%75%70%65%60%55%50%45%40%35%30%25%20%15%10% istributed on a Current Basis0%0%0%0%0%0%0%0%0%0%0%0%0%0%0%0%0%0%0%0 of CFO$400 M$400 M$400 M$400 M$400 M$400 M$400 M$400 M$400 M$400 M$400 M$400 M$400 M$400 M$400 M$400 M$400 M$400 M$400 M - 0.0530.1110.1760.250.3330.4290.5380.6670.8181.001.2221.501.8572.3333.004.005.6679.00 s st (Spread in bps)-150150150150150150150150150150200200200200300300300450 ent FeeN/A50 bps50 bps50 bps50 bps50 bps50 bps50 bps50 bps50 bps50 bps50 bps50 bps50 bps50 bps50 bps50 bps50 bps50 bps N/A3%3%3%3%3%3%3%3%3%3%3%3%3%3%3%3%3%3%3 N/A1M LIBOR1M LIBOR1M LIBOR1M LIBOR1M LIBOR1M LIBOR1M LIBOR1M LIBOR1M LIBOR1M LIBOR1M LIBOR1M LIBOR1M LIBOR1M LIBOR1M LIBOR1M LIBOR1M LIBOR1M LIBO @ t=0N/A5.85%5.85%5.85%5.85%5.85%5.85%5.85%5.85%5.85%5.85%5.85%5.85%5.85%5.85%5.85%5.85%5.85%5.85% (All Securities)7 Years7 Years7 Years7 Years7 Years7 Years7 Years7 Years7 Years7 Years7 Years7 Years7 Years7 Years7 Years7 Years7 Years7 Years7 Years
Dire ct ex posu re t o por tfol io of H F
Table 2
Distribution of Hedge Fund Strategies within Sample
The table shows the absolute and relative frequencies of each of the hedge fund strategies in our sample. Panel A describes the sample before the aggregation of certain strategies while Panel B presents the sample after aggregation.
Strategy Frequency Relative
Frequency Strategy Frequency Relative
frequency
1 Convertible Arbitrage 100 2.39% 1 Convertible Arbitrage 100 2.41%
2 Distressed Securities 112 2.68% 2 Distressed Securities 112 2.70%
3 Emerging Markets: Asia 88 2.11% 3 Equity Hedge 1359 32.78%
4 Emerging Markets: E. Europe/CIS 71 1.70% 4 Equity Market Neutral 263 6.34%
5 Emerging Markets: Global 109 2.61% 5 Equity Non-Hedge 135 3.26%
6 Emerging Markets: Latin America 26 0.62% 6 Event-Driven 248 5.98%
7 Equity Hedge 1359 32.52% 7 Foreign Exchange 75 1.81%
8 Equity Market Neutral 263 6.29% 8 Macro 293 7.07%
9 Equity Non-Hedge 135 3.23% 9 Managed Futures 299 7.21%
10 Event-Driven 248 5.93% 10 Market Timing 20 0.48%
11 Fixed Income: Arbitrage 75 1.79% 11 Merger Arbitrage 37 0.89%
12 Fixed Income: Convertible Bonds 25 0.60% 12 Relative Value Arbitrage 288 6.95%
13 Fixed Income: Diversified 86 2.06% 13 Short Selling 19 0.46%
14 Fixed Income: High Yield 67 1.60% 14 Emerging Markets 294 7.09%
15 Fixed Income: Mortgage-Backed 56 1.34% 15 Fixed Income 309 7.45%
16 Foreign Exchange 75 1.79% 16 Sectorial 295 7.12%
17 Macro 293 7.01% TOTAL 4146 100%
Table 3 Statistics of Hedge Fund Strategy Indexes Table 3 presents the descriptive statistics and the results of the Jarque-Bera (JB), Lilliefors, and Genest-Remillard (G & R) normality tests for every hedge fund strategy in the sample. Period 1 runs from February 1991 to January 2001, while period 2 covers the seven following years to January 2008. For both panels, the nature of the statistics appears on the left-hand-side and the strategies feature horizontally. The descriptive statistics are monthly and include the first four moments of the distributions, as well as the minimum and maximum returns. With regard to the tests for normality, the value of the test statistic and a dummy variable indicating whether or not the value is significant at a confidence level of 95% are presented*. The dummy variable equals 1 when the null hypothesis of normality is rejected. * P-values are available upon request.
Convert. Arbit.Dist. SecuritiesEquity HedgeE. Mkt NeutralEquity N- HedgeEvent- DrivenFXMacroMnged Fut.Market TimingMerger Arbit.Relat. Val Arbit.Short SellingEmerg. MktsFixed Inc.Sectorial Mean0.01190.01510.01800.01010.01650.01650.01610.01380.01460.01520.01180.0145-0.00390.02440.01090.0200 Standard deviation0.01160.02160.02730.01110.03550.02250.02060.02130.04560.02570.01180.01140.08280.06590.01140.0410 Skewness-0.19630.91820.0413-0.2320-0.6419-0.52841.52950.23410.95910.7721-2.5619-0.70810.1929-0.1586-0.6013-0.5642 Kurtosis5.35997.44894.10262.59465.80568.83997.60323.92695.95064.939119.34664.5014.88893.26566.26896.7705 Min-0.0321-0.0647-0.0809-0.0195-0.1473-0.0948-0.0204-0.0561-0.0924-0.0464-0.0684-0.0230-0.3036-0.1946-0.0377-0.1733 Max0.05100.10860.10250.03380.11160.10940.11780.08260.22810.11540.03930.04020.27830.18740.04500.1399 JB Test (df=2)28.62115.826.111.9047.60176.11152.745.3961.9330.721467.3221.3018.580.8660.6677.45 α=5% ; x≤ 5.991110111011111011 Lilliefors Test0.0070.0010.500.020.500.160.0010.170.040.160.0080.0030.0080.500.100.01 α=5% ; p-val≥ 5%1101001010111001 G & R Test0.000.000.890.090.590.010.000.190.010.060.000.000.000.950.040.02 α=5% ; p-val≥ 5%1100011010111011 Convert. Arbit.Dist. SecuritiesEquity HedgeE. Mkt NeutralEquity N- HedgeEvent- DrivenFXMacroMnged Fut.Market TimingMerger Arbit.Relat. Val Arbit.Short SellingEmerg. MktsFixed Inc.Sectorial Mean0.00640.01140.00860.00560.01030.00890.00690.00940.01050.00640.00520.00850.00490.01670.00670.0113 Standard deviation0.01110.01340.01800.00640.03450.0160.00990.01360.02790.02430.00860.00650.04700.02950.00830.0214 Skewness-0.4950-0.1774-0.6148-1.2205-0.4870-0.77191.4167-0.0101-0.0549-0.0420-0.1752-0.62530.1632-0.9236-0.6435-0.3815 Kurtosis3.54643.25462.94555.70642.72873.61335.96882.78942.73632.57603.93173.61922.82473.37253.43562.5501 Min-0.0284-0.0240-0.0414-0.0196-0.0774-0.0342-0.0067-0.0224-0.0570-0.0514-0.0210-0.0127-0.1013-0.0679-0.0176-0.0395 Max0.03390.04590.04440.01640.07740.03870.04440.04330.07190.05960.02600.02060.12810.06490.02360.0570 JB Test (df=2)4.480.675.3046.493.589.6658.950.160.290.653.476.820.4812.436.462.75 α=5% ; x≤ 5.990001011000010110 Lilliefors Test0.120.180.050.020.070.0030.0060.500.500.380.020.130.390.0010.090.15 α=5% ; p-val≥ 5%0011011000100100 G & R Test0.030.440.010.010.090.000.000.920.990.780.040.090.350.000.020.03 α=5% ; p-val≥ 5%1011011000100111
Period 1:120 months (February 1991 to January 2001) Period 2: 84 months (February 2001 to January 2008)
Table 4 Descriptive Statistics of Secondary Data The table presents the first four moments of the distribution as well as the maximum and minimum. The statistics appear on the vertical axis, while the time series feature horizontally. They are all presented on a monthly return basis. 1M LIBOR and 1M T-Bill are relative to the money market while the Russell 3000 is relative to the stock market. CDX.NA.IG_5Y and LUCI_OAS relate to the corporate credit market while the three whose title starts with USA are related to the U.S. government securities, 10- and 20-year maturities. For the 10-year maturity, on-the-run (on-t-r) and off-the-run (off-t-r) rates are presented. Table 5 Composition of Optimal Portfolios for Sets of Preferences E1, E2 and E3 hows the composition of optimal portfolios for the first three sets of preferences. All hedge fund strategies appear on the vertical axis and the different portfolios (set and diversification constraint) are presented horizontally. The sum of each column equals to 1, as the weights are listed as a proportion of the total value and are d between 0 and 1 (no-short constraint). Blanks refer to null allocations.
LIBOR 1MT-Bill 1MRussel 3000CDX.NA.IG_5Y*ªLUCI_OAS*USA_10Y (on-t-r)USA_10Y (off-t-r)USA_20Y Mean0.00260.00260.00154.494812.03870.00370.00370.0042 Variance1.87E-065.10E-070.00161.587514.61991.50E-071.60E-071.10E-07 Skewness0.19060.3597-0.47430.90610.7873-0.0265-0.03010.3986 Excess kurtosis-1.6071-1.22160.34731.485-0.5299-0.4791-0.5402-0.5446 Max0.00480.00420.08039.041721.78330.00450.00450.0049 Min0.00090.0016-0.10642.54197.51670.00280.00280.0036 * Data are shown in terms of spread in basis points. ª The statistics relative to this series are calculated from 58 months of available data.
Period 2: 84 months (February 2001 to January 2008) y <= 100% y <= 50% y <= 25% y <= 20%y <= 15%y <= 10%y <= 100%y <= 50%y <= 25%y <= 20% y <= 15%y <= 10%y <= 100%y <= 50%y <= 25%y <= 20%y <= 15%y <= 1 rbitrage0.02670.01240.08280.13640.13720.01500.07990.07750.05010.05010.05310.05100.0569 ties0.09410.09410.09880.11540.15000.10000.25000.20000.15000.10000.13260.13260.13470.13150.1340 0.11950.11950.20230.15790.15000.10000.12880.20000.15000.10000.06880.06880.06900.06780.0700 tral0.05220.17800.17740.05790.06590.04880.04880.05660.05030.0574 dge0.02700.01540.01540.01330.01480.0197 0.01750.01750.05370.04840.08890.00030.04360.03600.03600.02470.03530.0367 nge0.29860.29860.25000.20000.15000.10000.44180.44180.25000.20000.15000.10000.20550.20550.20180.20000.1500 0.00770.04540.0335 0.00130.01060.02410.11150.10000.05380.05380.06060.06020.0926 g0.04820.04820.05820.08290.10460.09260.04190.04210.25000.20000.15000.10000.16160.16160.16420.16330.1500 age0.05240.05240.06450.07770.10740.09490.09310.09350.00500.02260.02380.02260.02260.02530.02370.0248 Arbitrage0.31540.31540.25000.20000.15000.10000.01470.01570.02480.02710.04120.05310.04800.04800.04600.04880.0513 0.03440.03440.04750.04860.06290.05870.03070.03070.09140.11030.08500.09230.07390.07390.06810.07350.0782 kets0.01980.01980.02110.01280.02730.02710.02090.00090.01530.02680.02680.01590.02570.0199 0.02040.06350.06160.00110.02950.02790.02790.01980.02780.0337 0.00770.0230.02650.05050.02650.02660.02830.02830.01330.02630.0248
tegyE1: {α = 1; β = 0; γ = 0}E2: {α = 1;β = 1; γ = 0}E3: {α = 1; β = 1; γ = 0.75}
Table 6 Performance of Optimal Portfolios for Sets of Preferences E1, E2, E3 and E6 esents the descriptive statistics, the results of the Jarque-Bera (JB), Lilliefors, and Genest-Remillard (G & R) tests for normality and the performance measures of th os for sets 1, 2 and 3 of preference for the moments of distributions; the equally-weighted (EW) portfolio is also presented. Each of the indicators appears on t xis and the different portfolios (set of preference and diversification constraint) are presented horizontally. The descriptive statistics are monthly and include the first four e distributions, as well as the maximum and minimum returns. With regard to the tests for normality, the value of the test statistic and a dummy variable indicating not the value is significant at a confidence level of 95% are presented*. The dummy variable equals 1 when the null hypothesisof normality is rejected.The performa es (Sharpe, Treynor, Sortino, Modified Sharpe and Omega (Ω)) are also presented on a monthly basis. Minimal Accepted Return (MAR) levels of 0.8% and 1.2% mont d for the calculations of the Sortino ratio and the Omega measure. The Modified Sharpe is computed based on a Value-at-Risk calculation with a 95% confidence level. ilable upon request.
E6: E y <= 100% y <= 50% y <= 25% y <= 20%y <= 15%y <= 10%y <= 100%y <= 50%y <= 25%y <= 20%y <= 15% y <= 10%y <= 100%y <= 50%y <= 25%y <= 20%y <= 15%y <= 10%y = 6.25% 0.0080770.0080770.0080950.0080580.0082150.0080030.0063760.0063780.0079710.0081800.0079020.0081100.0080310.0080310.0079400.0080210.0080910.0081560.008597 4.78E-054.78E-055.60E-056.35E-056.94E-057.10E-053.81E-053.82E-057.04E-057.03E-056.86E-056.88E-056.90E-056.90E-056.92E-056.95E-057.18E-057.08E-059.88E- -0.3793-0.3793-0.4507-0.4436-0.4165-0.45820.24930.2492-0.0005-0.1584-0.1268-0.2366-0.1314-0.1314-0.0869-0.1205-0.1384-0.2457-0.4270 tosis0.25810.25810.36610.34420.26390.2604-0.1148-0.11600.18390.1600-0.1919-0.25060.01750.0175-0.02130.0046-0.1070-0.1832-0.0592 0.02240.02240.02390.02490.02680.02650.02280.02280.03000.02980.02770.02700.02780.02780.02790.02790.02800.02710.0291 -0.0113-0.0113-0.0133-0.0137-0.0139-0.0138-0.0068-0.0068-0.0149-0.0136-0.0110-0.0115-0.0126-0.0126-0.0124-0.0125-0.0118-0.0116-0.0150 2.252.253.313.172.673.180.920.920.120.440.351.000.240.240.110.200.310.962.57 5.99000000000000000000 t0.500.500.090.030.080.150.500.500.500.240.050.100.380.380.500.380.490.120.04 ≥ 5%000100000010000000 illard Test0.400.450.110.060.030.020.600.610.690.200.210.040.330.470.580.330.240.030.00 ≥ 5%000011000001000001 0.79720.79720.73930.68980.67850.64570.61740.61740.64460.67020.64470.66890.65830.65830.64660.65490.65250.66490.6070 0.07020.07020.05680.04810.04740.04610.79150.79810.05220.05530.10180.09160.05860.05860.06210.05970.06840.07310.0418 04.11994.11993.41383.00412.92662.66334.84784.84653.27733.23943.27023.32393.22843.22843.23393.21863.20023.20592.3109 Rf2.01982.01981.72761.55191.52631.38831.68411.68421.61071.61781.57711.62381.59321.59321.58081.58721.58511.58931.282 0.0041.25361.25361.09290.98960.98470.89100.81320.81361.00371.02890.97071.01530.99930.99930.98120.99440.99681.00400.8658 0.0080.01510.01510.01710.00980.03500.0005-0.3131-0.3128-0.00490.0301-0.01610.01820.00520.0052-0.01000.00350.01500.02540.0829 0.012-0.5255-0.5255-0.4957-0.4775-0.4495-0.4623-0.6963-0.6961-0.4793-0.4573-0.4834-0.4620-0.4733-0.4733-0.4814-0.4733-0.4610-0.4539-0.3614 0.016-0.7610-0.7610-0.7360-0.7178-0.6970-0.7016-0.8462-0.8461-0.7101-0.6996-0.7142-0.7033-0.7090-0.7090-0.7129-0.7084-0.6995-0.6971-0.6174 pe 95% (α=5%)1.32941.32941.03870.88470.85260.76061.11711.11690.93240.93820.87960.89520.91740.91740.90250.91100.88870.87780.6542 16.388516.388512.657010.867310.25169.013716.898216.885911.017410.565210.638110.700610.518610.518610.702410.491710.389810.15507.4065 )6.96546.96545.82725.20874.99064.63304.92594.92655.08425.10614.76114.87674.98924.98924.89244.95304.88284.85844.1459 4.22474.22473.73073.41953.34143.13042.68002.68123.29923.39723.10353.21123.28723.28723.20093.26383.21743.22722.9930 1.02881.02881.03371.01901.06821.00100.52190.52240.99121.05680.97111.03351.00971.00970.98171.00651.02761.04711.1620 0.21490.21490.23680.25480.28560.26390.10440.10460.29320.30020.26660.28120.28220.28220.27600.28290.29540.29180.3955 0.04430.04430.05250.06000.06830.06380.02080.02080.08080.07720.07050.07020.07660.07660.07640.07750.08020.07380.1117
E1: {α = 1;β = 0; γ = 0}E2: {α = 1; β = 1; γ = 0}E3: {α = 1; β = 1; γ = 0.75}
Table 7
Performance and Rank of Portfolios According to the Comprehensive Measures
The table shows the results, on a monthly basis, of the Sortino ratio, the Modified Sharpe ratio and the Omega measure (Ω) for all 30 optimal portfolios as well as the equally-weighted fund. The 31 portfolios and their characteristics (sets of preference and diversification constraint) appear on the vertical axis and the performance measures are presented horizontally. Minimal Accepted Return (MAR) levels of 0.8% and 1.2% monthly are used for the calculations of the Sortino ratio and the Omega measure. The Modified Sharpe was computed based on a Value-at-Risk calculation with a 95% confidence level. To the right of each measure is the rank of the portfolio for a given indicator; 1 indicates the best performing portfolio and 31, the worst performing one.
Table 8 Performance of CFOs 11, 15 and 18 Table 8 presents the descriptive statistics, the results of the Jarque-Bera (JB), Lilliefors, and Genest-Remillard (G & R) tests for normality and the performance measures of CFO structures 11 (panel A), 15 (Panel B) and 18 (Panel C) constructed from the 31 hedge fund portfolios. For each of the three CFO structures, the nature of the underlying portfolio (set of preference and diversification constraint) appears on the vertical axis and their statistics within the particular CFO structure are presented horizontally. As a reference, the value of the debt portion of the CFO’s $400 M and the all-in funding cost, in basis points over the 1M LIBOR, appear at the top of each panel. The descriptive statistics are monthly and include the first four moments of the distributions, as well as the minimum and maximum returns. With regard to the tests for normality, the value of the test statistic and a dummy variable indicating whether or not the value is significant at a confidence level of 95% are presented*. The dummy variable equals 1 when the null hypothesis of normality is rejected. The performance measures (Sharpe, Treynor, Sortino, Modified Sharpe and Omega (Ω)) are also presented on a monthly basis. For the Sortino ratio and the Omega measure, the calculations are made for Minimal Accepted Return (MAR) levels of 0.8% and 1.2% monthly. The Modified Sharpe is computed based on a VaR with a 95% confidence level. EhkMeanVarianceSkewnessExcess kurtosisJB α=5%Lilliefors α=5%G&R α=5%SharpeTreynorSortino MAR=0.008Sortino MAR=0.012 Modified Sharpe α=5%
Ω MAR=0.008Ω MAR=0.012 E1: {α=1; β=0;γ=0}y ≤ 100%0.00981.255E-04-0.2858-0.01360000.64720.06020.99630.7690.75091.50240.6018 y ≤ 50%0.00981.255E-04-0.2858-0.01360000.64720.06020.99630.7690.75091.50240.6018 y ≤ 25%0.00981.460E-04-0.40640.07520000.60170.04730.89770.7130.62161.46680.6245 y ≤ 20%0.00981.667E-04-0.41040.07620000.55860.03910.82310.66280.54441.40900.6377 y ≤ 15%0.01001.817E-04-0.4135-0.01910010.55240.03880.81730.66350.52921.44350.6826 y ≤ 10%0.00971.861E-04-0.4443-0.01230110.52250.03770.75530.61620.48021.35670.6439 E2: {α=1; β=1;γ=0}y ≤ 100%0.00711.157E-040.47340.25800000.4201-0.52350.59430.43900.47860.80590.3329 y ≤ 50%0.00711.158E-040.47290.25590000.4202-0.51810.59460.43930.47880.80640.3333 y ≤ 25%0.00961.858E-040.0043-0.20650000.51790.04280.81070.64200.54971.35310.6461 y ≤ 20%0.01001.817E-04-0.1852-0.27460000.54820.04670.84070.67390.56541.43380.6780 y ≤ 15%0.00951.808E-04-0.1361-0.46120100.51940.10510.78420.62470.52701.32070.6303 y ≤ 10%0.00991.794E-04-0.2355-0.53940010.54600.09090.82550.65960.54981.39600.6706 E3: {α=1;β=1; γ=0.75}y ≤ 100%0.00971.790E-04-0.1204-0.29060000.53590.04970.82160.65450.55851.37850.6504 y ≤ 50%0.00971.790E-04-0.1204-0.29060000.53590.04970.82160.65450.55851.37850.6504 y ≤ 25%0.00961.803E-04-0.0757-0.31150000.52360.05310.80190.63740.54591.33960.6350 y ≤ 20%0.00971.803E-04-0.1110-0.30040000.53290.05080.81700.65090.55471.37180.6497 y ≤ 15%0.00981.864E-04-0.1286-0.38600000.53260.06090.81700.65280.54831.38680.6698 y ≤ 10%0.00991.835E-04-0.2351-0.46670110.54480.06680.82580.66150.54761.41110.6826 E4: {α=2;β=1; γ=0.75}y ≤ 100%0.00971.791E-04-0.1920-0.18830000.53660.04220.81390.65160.54731.38290.6489 y ≤ 50%0.00971.791E-04-0.1920-0.18830000.53660.04220.81390.65160.54731.38290.6489 y ≤ 25%0.00971.775E-04-0.1939-0.18860000.53930.04290.81850.65460.55171.38580.6481 y ≤ 20%0.00981.803E-04-0.1847-0.20760000.53600.04310.81450.65190.54731.38400.6521 y ≤ 15%0.01001.870E-04-0.1854-0.30370000.54060.04910.82830.66350.55131.41870.6849 y ≤ 10%0.01001.864E-04-0.2818-0.36140110.54630.05310.82580.66390.54121.42940.6959 E5: {α=3;β=1; γ=0.25}y ≤ 100%0.00741.159E-040.3280-0.03880000.44880.26280.63980.47470.50980.86890.3538 y ≤ 50%0.00741.159E-040.3277-0.03810000.44960.26370.64120.47570.51110.87040.3543 y ≤ 25%0.00971.890E-040.0167-0.18730000.52250.04030.82510.65360.55871.38060.6639 y ≤ 20%0.01001.899E-04-0.1505-0.22020000.53640.04040.82710.66370.55121.42560.6860 y ≤ 15%0.01001.872E-04-0.2307-0.25060000.54300.04560.82710.66500.54701.42850.6887 y ≤ 10%0.00991.795E-04-0.2604-0.39250110.54970.07050.83130.66540.55221.41370.6768 E6: EW (1/m)y = 6.25%0.01062.565E-04-0.3987-0.19210110.50330.03450.75220.62830.44911.48540.8058
CFO 11 (Debt = $200 M ; All-in funding cost = 150 bps over LIBOR 1 month)PANEL A
Table 8 Performance of CFOs 11, 15 and 18 (continued) EhkMeanVarianceSkewnessExcess kurtosisJB α=5%Lilliefors α=5%G&R α=5%SharpeTreynorSortino MAR=0.008Sortino MAR=0.012 Modified Sharpe α=5%
Ω MAR=0.008Ω MAR=0.012 E1: {α=1;β=0;γ=0}y ≤ 100%0.01202.540E-04-0.1768-0.08260000.59360.05680.99840.82120.62691.87391.0037 y ≤ 50%0.01202.540E-04-0.1768-0.08260000.59360.05680.99840.82120.62691.87391.0037 y ≤ 25%0.01202.953E-04-0.34330.01780000.55200.04350.88550.74640.52211.79751.0072 y ≤ 20%0.01203.400E-04-0.36460.04350000.51040.03540.80340.68470.45711.69780.9963 y ≤ 15%0.01233.710E-04-0.3883-0.04600110.50470.03510.79300.68010.44301.71621.0374 y ≤ 10%0.01193.789E-04-0.4098-0.07140110.47790.03420.73470.63190.40631.62070.9830 E2: {α=1;β=1;γ=0}y ≤ 100%0.00822.646E-040.65830.64941000.3473-0.23640.55180.44120.34761.03430.5617 y ≤ 50%0.00822.647E-040.65770.64681010.3475-0.23500.55220.44160.34781.03490.5621 y ≤ 25%0.01183.824E-040.0606-0.30490000.47030.03900.79010.66570.45521.62780.9696 y ≤ 20%0.01223.666E-04-0.1560-0.42770000.50350.04310.82480.69910.47321.71071.0270 y ≤ 15%0.01173.664E-04-0.0863-0.53610110.47620.11540.77420.65170.44461.58210.9598 y ≤ 10%0.01213.595E-04-0.1839-0.66450110.50420.09570.82140.69140.46861.66621.0157 E3: {α=1;β=1;γ=0.75}y ≤ 100%0.01193.594E-04-0.0623-0.40810000.49350.04660.81470.68550.47331.65590.9894 y ≤ 50%0.01193.594E-04-0.0623-0.40810000.49350.04660.81470.68550.47331.65590.9894 y ≤ 25%0.01173.626E-04-0.0169-0.42770000.48140.05030.79520.66760.46171.61030.9655 y ≤ 20%0.01193.620E-04-0.0530-0.41790000.49070.04790.81030.68160.47021.64810.9868 y ≤ 15%0.01213.736E-04-0.0663-0.48510000.49140.05930.81230.68410.46791.65571.0078 y ≤ 10%0.01223.663E-04-0.1794-0.59680110.50410.06600.82250.69420.46911.68291.0269 E4: {α=2;β=1;γ=0.75}y ≤ 100%0.01193.607E-04-0.1434-0.31670000.49320.03870.80230.67860.46231.66230.9907 y ≤ 50%0.01193.607E-04-0.1434-0.31670000.49320.03870.80230.67860.46231.66230.9907 y ≤ 25%0.01193.570E-04-0.1445-0.32040000.49590.03940.80780.68250.46621.66750.9913 y ≤ 20%0.01203.624E-04-0.1323-0.33540000.49320.03960.80450.67990.46361.66220.9938 y ≤ 15%0.01223.729E-04-0.1244-0.42740000.50010.04620.82440.69620.47251.69621.0282 y ≤ 10%0.01233.709E-04-0.2267-0.49160110.50630.05060.82290.69680.46581.70891.0403 E5: {α=3;β=1;γ=0.25}y ≤ 100%0.00872.595E-040.49000.24610000.37840.36340.60230.48260.37991.10960.5994 y ≤ 50%0.00872.594E-040.49020.24750000.37920.36580.60390.48380.38101.11150.6002 y ≤ 25%0.01193.888E-040.0769-0.26800000.47500.03650.80480.67810.46371.65520.9910 y ≤ 20%0.01223.844E-04-0.1036-0.33330000.49220.03690.81160.68890.46441.70131.0274 y ≤ 15%0.01233.732E-04-0.1756-0.38960000.50250.04250.82170.69590.46881.70501.0348 y ≤ 10%0.01223.569E-04-0.1913-0.52830110.50970.07050.83190.70100.47651.69171.0250 E6: EW (1/m)y = 6.25%0.01315.175E-04-0.3569-0.11350110.46480.03150.73500.64290.39091.71741.1298
CFO 15 (Debt = $280 M ; All-in funding cost = 200 bps over LIBOR 1 month)PANEL B
Table 8 Performance of CFOs 11, 15 and 18 (continued) * P-values are available upon request.
EhkMeanVarianceSkewnessExcess kurtosisJB α=5%Lilliefors α=5%G&R α=5%SharpeTreynorSortino MAR=0.008Sortino MAR=0.012 Modified Sharpe α=5%
Ω MAR=0.008Ω MAR=0.012 E1: {α=1;β=0;γ=0}y ≤ 100%0.01496.779E-04-0.01870.09590000.47490.04740.83140.73260.44181.95851.3345 y ≤ 50%0.01496.779E-04-0.01870.09590000.47490.04740.83140.73260.44181.95851.3345 y ≤ 25%0.0157.978E-04-0.26320.27700000.43940.03480.72370.64970.36821.86081.3082 y ≤ 20%0.01499.408E-04-0.31930.34990000.40180.02760.64450.58390.31961.74551.2680 y ≤ 15%0.01541.038E-03-0.36880.30020000.39740.02750.63250.57590.30921.75141.2960 y ≤ 10%0.01471.047E-03-0.37400.16570100.37640.02670.58910.53660.28701.66421.2325 E2: {α=1;β=1;γ=0}y ≤ 100%0.00878.573E-040.86881.27821110.2080-0.09900.34330.30040.17621.06000.7474 y ≤ 50%0.00878.573E-040.86821.27481110.2082-0.09860.34380.30080.17641.06070.7479 y ≤ 25%0.01461.092E-030.1824-0.08110000.36320.03060.62590.56330.31351.66291.2187 y ≤ 20%0.01521.004E-03-0.0837-0.30540000.39960.03470.66820.60240.33431.75381.2895 y ≤ 15%0.01459.800E-040.0330-0.40120000.37990.12860.63790.57070.32141.64251.2108 y ≤ 10%0.01519.415E-04-0.0809-0.66260110.40960.09780.68930.61570.34441.73111.2769 E3: {α=1;β=1;γ=0.75}y ≤ 100%0.01489.627E-040.0564-0.37230000.39430.03850.67260.60130.34001.71031.2484 y ≤ 50%0.01489.627E-040.0564-0.37230000.39430.03850.67260.60130.34001.71031.2484 y ≤ 25%0.01459.726E-040.1058-0.42540000.38320.04210.65530.58460.33041.66371.2176 y ≤ 20%0.01489.691E-040.0682-0.38870000.39210.03970.66930.59810.33811.70271.2436 y ≤ 15%0.01509.911E-040.0678-0.42400010.39600.05230.67810.60590.34211.71251.2634 y ≤ 10%0.01539.583E-04-0.0742-0.62600000.41010.06000.69150.61870.34561.74651.2889 E4: {α=2;β=1;γ=0.75}y ≤ 100%0.01489.786E-04-0.0544-0.23810000.39160.03070.65380.58760.32851.71001.2484 y ≤ 50%0.01489.786E-04-0.0544-0.23810000.39160.03070.65380.58760.32851.71001.2484 y ≤ 25%0.01489.663E-04-0.0537-0.25160000.39430.03130.65950.59220.33161.71621.2506 y ≤ 20%0.01499.791E-04-0.0351-0.27270000.39270.03160.65860.59120.33111.71121.2508 y ≤ 15%0.01539.873E-04-0.0033-0.39390100.40420.03850.68910.61710.34611.75371.2874 y ≤ 10%0.01549.708E-04-0.1297-0.50040000.41250.04320.69230.62100.34391.77101.3017 E5: {α=3;β=1;γ=0.25}y ≤ 100%0.00948.231E-040.71120.83571000.23950.72320.39670.34680.20531.13710.7980 y ≤ 50%0.00958.222E-040.71200.83811000.24030.74330.39840.34820.20611.13930.7993 y ≤ 25%0.01481.111E-030.1996-0.00700000.36800.02840.63860.57490.32031.68941.2410 y ≤ 20%0.01531.059E-03-0.0150-0.16750000.39010.02920.65760.59350.32951.74251.2836 y ≤ 15%0.01539.901E-04-0.0701-0.35560000.40610.03490.68450.61450.34261.75941.2945 y ≤ 10%0.01529.250E-04-0.0578-0.55210010.41650.06540.70570.62980.35531.76021.2916 E6: EW (1/m)y = 6.25%0.01671.412E-03-0.32070.38040000.37710.02550.60700.55880.29061.75991.3623
CFO 18 (Debt = $340 M ; All-in funding cost = 300 bps over LIBOR 1 month)PANEL C
Table 9 Results of Multivariate Linear Regressions for CFOs 1, 11, 15 and 18 hows the results of the multivariate linear regression model applied to the returns of CFO structures 1, 11, 15 and 18. For every structure, the value of the coefficie e to each independent variable and their corresponding p-value are presented. The coefficient δ is the model’s constant. Within each panel (A to D), the indepen appear on the vertical axis and the underlying funds (set of preference and diversification constraint) are presented horizontally. The shaded values indicate ap-v
{α=1; β=0; γ=0} y ≤ 100%{α=1; β=1; γ=0} y ≤ 100%{α=1;β=1; γ=0} y ≤ 20%{α=2; β=1; γ=0.75} y ≤ 10%{α=3; β=1; γ=0.25} y ≤ 50%{α=3; β=1; γ=0.25} y ≤ 15%1/m y = 6.25% 0.0258180.0211770.0245430.0256770.0203730.0261330.026712 0.061247-0.0084930.0822770.0770320.0069840.0874230.129787 -0.000675-0.000480-0.000671-0.000603-0.000451-0.000659-0.000639 -21.324371-20.243579-11.967612-21.047440-20.423683-17.897796-16.064178 -2.305055-2.320236-2.013981-2.712104-2.214730-2.580198-2.646475 -0.000144-0.000127-0.000122-0.000143-0.000116-0.000142-0.000151 {α=1; β=0; γ=0} y ≤ 100%{α=1; β=1; γ=0} y ≤ 100%{α=1;β=1; γ=0} y ≤ 20%{α=2; β=1; γ=0.75} y ≤ 10%{α=3; β=1; γ=0.25} y ≤ 50%{α=3; β=1; γ=0.25} y ≤ 15%1/m y = 6.25% 0.00000.00020.00050.00040.00050.00020.0005 0.00160.65360.00060.00180.71770.00030.0000 0.00970.06490.03530.06710.08890.03980.0677 0.35500.38300.67230.47340.38860.52970.6060 0.05110.05120.16330.07130.06780.07700.0969 0.00140.00490.02490.01190.01120.00980.0123
PANEL A CFO 1 (Direct exposure to Portfolio of HF) coefficients p-values
{α=1; β=0; γ=0} y ≤ 100%{α=1; β=1; γ=0} y ≤ 100%{α=1; β=1; γ=0} y ≤ 20%{α=2; β=1; γ=0.75} y ≤ 10%{α=3; β=1; γ=0.25} y ≤ 50%{α=3; β=1; γ=0.25} y ≤ 15%y = 6.25% δ0.0379320.0317450.0358750.0376320.0301350.0383190.038 STOCK0.098863-0.0229170.1346740.1226590.0041860.1422370.217 DEF-0.001056-0.000803-0.001073-0.000942-0.000749-0.001033-0.0009 LIQU-49.959631-46.930344-35.537299-49.574431-48.093856-45.137863-41 TERM-3.254628-3.444272-2.654086-3.858305-3.212852-3.641032-3.6064 TREND-0.000253-0.000230-0.000217-0.000250-0.000211-0.000249-0.0002 {α=1; β=0; γ=0} y ≤ 100%{α=1; β=1; γ=0} y ≤ 100%{α=1; β=1; γ=0} y ≤ 20%{α=2; β=1; γ=0.75} y ≤ 10%{α=3; β=1; γ=0.25} y ≤ 50%{α=3; β=1; γ=0.25} y ≤ 15%y = 6.25% δ0.00000.00130.00130.00110.00240.00060.00 STOCK0.00150.48480.00050.00190.89910.00020.00 DEF0.01190.07440.03530.07380.09860.04290.08 LIQU0.17940.24370.43260.29250.23620.32050.39 TERM0.08610.09350.24950.10820.12030.11620.15 TREND0.00050.00320.01310.00610.00730.00470.00
PANEL B p-values
coefficientsCFO 11 {α=1; β=0; γ=0} y ≤ 100%{α=1; β=1; γ=0} y ≤ 100%{α=1;β=1; γ=0} y ≤ 20%{α=2; β=1; γ=0.75} y ≤ 10%{α=3; β=1; γ=0.25} y ≤ 50%{α=3; β=1; γ=0.25} y ≤ 15%1/m y = 6.25% 0.0508560.0442290.0480160.0503080.0414760.0512770.049340 0.138615-0.0442030.1919640.169802-0.0034300.2012550.316547 -0.001428-0.001170-0.001481-0.001271-0.001080-0.001401-0.001199 -81.254411-76.995044-62.397691-80.775945-79.772810-75.565411-69.526505 -4.251777-4.744886-3.253458-5.024286-4.336980-4.723197-4.471656 -0.000370-0.000350-0.000320-0.000366-0.000318-0.000364-0.000368 {α=1; β=0; γ=0} y ≤ 100%{α=1; β=1; γ=0} y ≤ 100%{α=1;β=1; γ=0} y ≤ 20%{α=2; β=1; γ=0.75} y ≤ 10%{α=3; β=1; γ=0.25} y ≤ 50%{α=3; β=1; γ=0.25} y ≤ 15%1/m y = 6.25% 0.00010.00280.00220.00190.00480.00110.0037 0.00170.37120.00040.00230.94450.00020.0000 0.01630.08410.04010.08680.11020.05070.1235 0.12450.20430.33110.22430.18850.23780.3185 0.11350.12430.31830.13750.15940.14700.2073 0.00040.00290.00990.00450.00660.00340.0064
PANEL C coefficientsCFO 15 p-values
{α=1; β=0; γ=0} y ≤ 100%{α=1; β=1; γ=0} y ≤ 100%{α=1;β=1; γ=0} y ≤ 20%{α=2; β=1; γ=0.75} y ≤ 10%{α=3; β=1; γ=0.25} y ≤ 50%{α=3; β=1; γ=0.25} y ≤ 15%y = 6 δ0.0740280.0706760.0699720.0728360.0646120.0746300.06 STOCK0.218948-0.0990100.3139630.262845-0.0277300.3240060.534 DEF-0.002167-0.002082-0.002329-0.001924-0.001884-0.002143-0.00 LIQU-146.250322-145.031986-121.184595-145.829989-152.364230-140.468397-126.84 TERM-6.021820-7.488111-4.120773-7.066956-6.627699-6.635288-5.64 TREND-0.000590-0.000613-0.000512-0.000579-0.000546-0.000579-0.00 {α=1; β=0; γ=0} y ≤ 100%{α=1; β=1; γ=0} y ≤ 100%{α=1;β=1; γ=0} y ≤ 20%{α=2; β=1; γ=0.75} y ≤ 10%{α=3; β=1; γ=0.25} y ≤ 50%{α=3; β=1; γ=0.25} y ≤ 15%y = 6 δ0.00050.00750.00680.00560.01330.00340.01 STOCK0.00260.26600.00050.00370.75240.00030.00 DEF0.02640.08730.05140.11130.11780.06710.21 LIQU0.09340.18380.25590.17860.15920.18010.27 TERM0.17230.17660.44570.19900.22690.21190.33 TREND0.00050.00370.01270.00570.00880.00430.01
PANEL D p-values
coefficientsCFO 18