معیار سهام خصوصی و بهینه سازی سبد سرمایه گذاری

Portfolio optimization using private equity is typically based on one of three indices: listed private equity, transaction-based private equity, or appraisal value-based private equity indices. However, we show that none of these indices is fully suitable for portfolio optimization. We introduce here a new benchmark index for venture capital and buyouts, which is updated monthly, adjusted for autocorrelation (de-smoothing), and available contemporaneously. We illustrate how our benchmark enables superior quantitative portfolio optimization.

Private equity (PE) has played an increasingly important role in the portfolios of institutional investors such as endowments, pension funds, insurance companies, and high net worth individuals (see, e.g., Keuschnigg and Nielsen, 2003, Kanniainen and Keuschnigg, 2004, Nahata, 2008, Groh et al., 2010a and Groh et al., 2010b; and Groh and Liechtenstein, 2011a, Groh and Liechtenstein, 2011b and Groh and Liechtenstein, 2011c). In fact, according to the Boston Consulting Group (2009), as of year-end 2009, approximately US $1 trillion was invested in PE. However, institutional investments in PE are both long-term and illiquid, and it is thus somewhat difficult to establish optimal portfolio weights, particularly relative to more liquid asset classes. The importance of benchmarking PE investments in theory and in practice cannot be overstated. Recent work by Groh et al. (2012) focuses on benchmarking PE at a country level. This issue is followed closely by institutional investors worldwide,3 who require representative benchmarks or PE indices in order to determine the optimal proportion of PE to be allocated to their portfolios (see, e.g., Woodward and Hall, 2003, Woodward, 2004 and Tierney and Bailey, 1997; and Nesbitt and Reynolds, 1997). Moreover, suitable benchmarks are also needed to calculate risk exposures, such as value-at-risk (VaR) or conditional VaR, and risk capital requirements, such as those mandated under Basel III. Without appropriate benchmarks, institutional investors are at risk of misallocating their capital to the PE asset class as a whole, as well as among various PE funds. Benchmarking, therefore, is fundamental to the entire PE market and all firms and stakeholders connected with it. It can be considered one of the most important aspects of PE research. This paper addresses several interrelated issues. First, are institutional investors using the most appropriate PE benchmarks in portfolio optimization? Second, if not, what are the most appropriate benchmarks? And third, how large are the differences in portfolio construction for the appropriate versus inappropriate PE benchmarks? Institutional investors generally use one of three concepts when constructing PE indices: (1) listed PE indices, (2) transaction-based PE indices, and (3) appraisal value-based PE indices. Each index has advantages and disadvantages for capturing PE risk/return profiles. In this paper, we show, however, that none of the indices fully captures appropriately input quantities for portfolio optimization or for risk models. For example, listed PE indices contain up-to-date data, but are insufficient for portfolio optimization because they overestimate the volatility of the underlying investments, and hence underestimate the optimal percentage of PE to be allocated to a given portfolio. Transaction-based indices, on the other hand, use realized cash flows of prior PE transactions, but the time lag of their data availability is suboptimal, and they may thus misallocate portfolio weights, particularly during financial crises. Meanwhile, appraisal value-based PE indices use quarterly evaluations of the book value of PE portfolio companies, along with changes in actual cash flow. But they likewise feature a time lag in data availability, and may also have appraisal-smoothing problems. A mismatch in data timing and smoothed returns can create spurious portfolio optimization results. Thus, none of the three index concepts currently in popular use is fully capable of capturing the risk/return profile of PE, and none provides the necessary input quantities for portfolio optimization or risk models. We elaborate on this point further in the first part of this paper. We also improve upon these methods by introducing a new representative benchmark for PE that specifically considers segments of the PE asset class for venture capital and buyouts as a means to more appropriately capture the risk/return profile. Our new benchmark index works as follows. We first calculate appraisal value-based PE benchmarks using those indices. We rescale quarterly returns to monthly returns by using Getmansky et al.’s (2004) method, which corrects for positive autocorrelation in returns (see also Koijen et al., 2009). Second, we use capital market information in a forecast model that includes listed PE and macroeconomic variables in order to close the quarterly time gap and obtain up-to-date performance. In our final step, we calculate a superior benchmark that features monthly frequency and contemporary performance reporting. We demonstrate that our new benchmark is suitable for use in portfolio optimization and risk models. Because portfolio optimization varies in an economically significant way in relation to index choice, we find that our new index provides a quantitative improvement. Furthermore, by using a Monte Carlo simulation and historical US returns from the January 1999-December 2008 period, we show that the portfolio exhibits statistically significantly higher levels of risk when listed PE is used as a proxy than when our modified appraisal value-based benchmark is used. We also find lower stated Sharpe ratios when using listed PE than when we use our modified appraisal value-based benchmark. This choice could cause disproportionately low levels of new capital inflows compared to peers that use the appropriate PE benchmarks for performance assessment. Overall, our results confirm that our new index improves risk management for PE limited partners, thus facilitating the flow of funds into the PE industry. The remainder of this paper is structured as follows. Section 2 describes the different index concepts. Section 3 introduces our methodology for constructing the appraisal value-based PE benchmarks, and presents the results of the forecast model. Section 4 demonstrates the impact of index selection on the resulting asset allocation. Section 5 concludes, and provides a summary of our most important findings.

Portfolio optimization with PE in practice has been based on one of three indices: listed PE, transaction-based PE, or appraisal value-based PE. This paper explains why these indices are insufficient for portfolio optimization. We also illustrate how we can calculate adequate benchmarks for different PE segments by using appraisal value-based PE Indices. Our benchmarks, in comparison to the three indices commonly used now, have the advantages of being (1) available on a monthly basis, (2) desmoothed for autocorrelation, and 93) up-to-date. To close the one-quarter gap, we used a forecasting model (e.g., a point estimator), flanked by an up and down confidence band, in order to estimate the best and worst case developments meaningfully and conservatively. Our benchmarks meet all the demands necessary to serve as adequate input quantities in portfolio optimization or for risk models. We further show that the choice of PE proxy has a major impact on portfolio performance and risk/return profile. The index we develop here would yield more accurate financial reporting and portfolio optimization than those currently in use. This accuracy would in turn facilitate the development of PE markets and appropriate institutional risk management for PE limited partners. The empirical methods we develop can be applied in future work to PE, as well as to other illiquid alternative investment markets, such as art, real estate, and timber, among others.