Estimating cost of capital in firm valuations with arithmetic or geometric mean – or better use the Cooper estimator?

We test the extent and determinants of bias effects of the arithmetic as well as the geometric mean estimator and the estimator of Cooper [1996. Arithmetic versus geometric mean estimators: Setting discount rates for capital budgeting. European Financial Management 2 (July): 157–67] regarding discount rate estimation for firm valuation by way of a bootstrap approach for 13 different countries. The Cooper estimator is superior to both the geometric and the (conventional) arithmetic mean estimator. However, a ‘truncated’ version of the arithmetic mean estimator leads generally to better estimation outcomes than the Cooper estimator. This means that, in order to reduce problems of upward-biased firm value estimates, expected cash flows beyond a certain time horizon are completely neglected in terminal value estimation. Such an approach seems particularly reasonable for the valuation of young growth companies as well as for companies from quickly developing countries such as Brazil, China, or Thailand, because the bias in terminal value estimation is increasing in the growth rate of future expected cash flows.     

Nonparametric Estimation of Expected Shortfall

The expected shortfall is an increasingly popular risk measurein financial risk management and it possesses the desired sub-additivityproperty, which is lacking for the value at risk (VaR). We considertwo nonparametric expected shortfall estimators for dependentfinancial losses. One is a sample average of excessive losseslarger than a VaR. The other is a kernel smoothed version ofthe first estimator (Scaillet, 2004 Mathematical Finance), hopingthat more accurate estimation can be achieved by smoothing.Our analysis reveals that the extra kernel smoothing does notproduce more accurate estimation of the shortfall. This is differentfrom the estimation of the VaR where smoothing has been shownto produce reduction in both the variance and the mean squareerror of estimation. Therefore, the simpler ES estimator basedon the sample average of excessive losses is attractive forthe shortfall estimation.     

Estimating Systematic Risk with Daily Security Returns: A Note on the Relative Efficiency of Selected Estimators

This paper utilizes asymptotic analysis and daily security returns to examine the estimation efficiency of two unbiased robust estimators compared with ordinary least squares. Our results demonstrate a relative efficiency gain for a nonparametric rank estimator and a relative efficiency loss for the minimum absolute deviation estimator when estimating the systematic risk of securities using daily security returns.     

Moments of multivariate regime switching with application to risk-return trade-off

We use a Fourier transform to derive multivariate conditional and unconditional moments of multi-horizon returns under a regime-switching model. These moments are applied to examine the relevance of risk horizon and regimes for buy-and-hold investors. We analyze the impact of time-varying expected returns and risk (variance and covariance) on portfolio allocations' “term structure”—portfolio allocations as a function of the investment horizon. Using monthly observations on S&P composite index and 10-year Government Bond, we find that the term structure of the optimal allocations depends on market conditions measured by the probability of being in bull state. At short horizons and when this probability is low, buy-and-hold investors decrease their holdings of risky assets. We also find that the conditional optimal portfolio performs quite well at short and intermediate horizons and less at long horizons.     

Dynamic asset–liability management in a Markov market with stochastic cash flows

This paper provides a general model to investigate an asset–liability management (ALM) problem in a Markov regime-switching market in a multi-period mean–variance (M–V) framework. Emphasis is placed on the stochastic cash flows in both wealth and liability dynamic processes, and the optimal investment and liquidity management strategies in achieving the M–V bi-objective of terminal surplus are evaluated. In this model, not only the asset returns and liability returns, but also the cash flows depend on the stochastic market states, which are assumed to follow a discrete-time Markov chain. Adopting the dynamic programming approach, the matrix theory and the Lagrange dual principle, we obtain closed-form expressions for the efficient investment strategy. Our proposed model is examined through empirical studies of a defined contribution pension fund. In-sample results show that, given the same risk level, an ALM investor (a) starting in a bear market can expect a higher return compared to beginning in a bull market and (b) has a lower expected return when there are major cash flow problems. The effects of the investment horizon and state-switching probability on the efficient frontier are also discussed. Out-of-sample analyses show the dynamic optimal liquidity management process. An ALM investor using our model can achieve his or her surplus objective in advance and with a minimum variance close to zero.     

Assessing the Economic Significance of Return Predictability: A Research Note

The predictability of stock returns is often assessed using classical statistical significance from predictive regressions. Statistical inference, however, can belie the economic importance with which investors regard various predictors. This paper examines the influence that predictors have on an investor's optimal portfolio allocations. The results show that return predictability is sufficient to induce horizon effects in optimal allocations. After incorporating estimation risk, however, little evidence of predictability remains. We also assess the relative importance of three predictor variables. While dividend yield is the most important predictor, optimal allocations are also sensitive to the term spread and the relative bill rate.     

Are Stocks Really Less Volatile in the Long Run?

According to conventional wisdom, annualized volatility of stock returns is lower over long horizons than over short horizons, due to mean reversion induced by return predictability. In contrast, we find that stocks are substantially more volatile over long horizons from an investor's perspective. This perspective recognizes that parameters are uncertain, even with two centuries of data, and that observable predictors imperfectly deliver the conditional expected return. Mean reversion contributes strongly to reducing long‐horizon variance but is more than offset by various uncertainties faced by the investor. The same uncertainties reduce desired stock allocations of long‐horizon investors contemplating target‐date funds.     

Mean Reversion in the Short Horizon Returns of UK Portfolios

This paper will show that short horizon stock returns for UK portfolios are more predictable than suggested by sample autocorrelation co-efficients. Four capitalisation based portfolios are constructed for the period 1976–1991. It is shown that the first order autocorrelation coefficient of monthly returns can explain no more than 10% of the variation in monthly portfolio returns. Monthly autocorrelation coefficients assume that each weekly return of the previous month contains the same amount of information. However, this will not be the case if short horizon returns contain predictable components which dissipate rapidly. In this case, the return of the most recent week would say a lot more about the future monthly portfolio return than other weeks. This suggests that when predicting future monthly portfolio returns more weight should be given to the most recent weeks of the previous month, because, the most recent weekly returns provide the most information about the subsequent months' performance. We construct a model which exploits the mean reverting characteristics of monthly portfolio returns. Using this model we forecast future monthly portfolio returns. When compared to forecasts that utilise the autocorrelation statistic the model which exploits the mean reverting characteristics of monthlyportfolio returns can forecast future returns better than the autocorrelation statistic, both in and out of sample.     

Hedging Housing Risk*

An unusually rich source of data on housing prices in Stockholm is used to analyze the investment implications of housing choices. This empirical analysis derives market-wide price and return series for housing investment during a 13-year period, and it also provides estimates of the individual-specific, idiosyncratic, variation in housing returns. Because the idiosyncratic component follows an autocorrelated process, the analysis of portfolio choice is dependent upon the holding period. We analyze the composition of household investment portfolios containing housing, common stocks, stocks in real estate holding companies, bonds, and t-bills. For short holding periods, the efficient portfolio contains essentially no housing. For longer periods, low-risk portfolios contain 15 to 50 percent housing. These results suggest that there are large potential gains from policies or institutions that would permit households to hedge their lumpy investments in housing. We estimate the potential value of hedges in reducing risk to households, yet yielding the same investment returns. The value is surprisingly large, especially to poorer homeowners.     

The impact of portfolio diversification on mean reverting components of stock indices

Positive autocorrelations are introduced into stock index portfolios when they are formed from individual stock indices while negative autocorrelations are induced in returns by increasing the investment horizon. Using monthly data of six international stock indices, this paper examines the diversification effect with different investment horizons on autocorrelations of stock index portfolios. The results show that portfolio diversification does not alter the impact of the investment horizon on autocorrelations. Different investment horizons, however, have great impact on the diversification effect on autocorrelations. With short (long) horizons, the average autocorrelation coefficient increases (decreases) with an increase in the portfolio size, suggesting that mean-reverting component dominates the delayed adjustment effect in long horizons and vice versa in short horizons. Our results are robust across two 10-year sub-periods.The author would like to thank an anonymous referee of this Journal for the comments on an earlier version of this paper and the Research Committee of Hong Kong Baptist University for the financial support in this research.     

Country and currency diversification of bond investments: do they really make sense for Swiss investors?

The inclusion of hedged or unhedged foreign currency bonds within a strategic asset allocation is a crucial decision which should be analyzed carefully. The goal of this paper is to provide a contribution to this analysis by focusing particularly on the time horizon of the investment. Results are analyzed from the perspective of a Swiss investor. We find that over the last 21 years, investing in bonds denominated in Swiss Francs has been clearly less efficient in terms of risk-adjusted returns than investing in a hedged global bond portfolio. For short-term investors, we find robust evidence against the hypothesis of investing in unhedged foreign currency bonds. The picture changes dramatically, however, when we consider an investment horizon of 6 years and the normal case of balanced portfolios including also equities and domestic bonds. In this case, the optimal strategy for the period we analyzed would have been to hedge only the exposure to US dollar bonds.      

Insider Investment Horizon

We examine the relation between insiders’ investment horizon and the information content of their trades with respect to future stock returns. We conjecture that an insider's investment horizon establishes a benchmark for expected patterns of continued trading behavior and thus helps identify unexpected insider trades, which should be more informative in efficient markets. Consistent with this conjecture, the trades of short-horizon insiders are both more unexpected and more informed, on average, than those of long-horizon insiders. Short-horizon insiders and their firms also tend to display characteristics that are associated with a greater focus on short-termism.     

Arithmetic versus geometric mean estimators: Setting discount rates for capital budgeting

This paper addresses an issue central to the estimation of discount rates for capital budgeting: should the geometric mean or arithmetic mean of past data be used when estimating the discount rate? the use of the arithmetic mean ignores estimation error and serial correlation in returns. Unbiased discount factors have been derived that correct for both these effects. In all cases, the corrected discount rates are closer to the arithmetic than the geometric mean.     

Downside Risk and Investment Choice

This paper develops an optimal investment strategy for individuals concerned with avoiding the possibility of realizing returns below a predetermined target level within a prescribed period of time. Assuming a Brownian motion process, a model is developed which allows computation of the exact probability of failure. The algorithm and associated comparative statics with respect to the mean and standard deviation of returns, target return, time horizon, and risk-free rate of return are likely to have many useful practical applications.     

Riding the yield curve: a spanning analysis

The average return on long-term bonds exceeds the return on short-term bills by a large amount over short investment horizons. A riding-the-yield-curve investment strategy takes advantage of the higher returns on longer term bonds. This strategy involves the purchase of bonds with maturities longer than the investment horizon and the sale of these bonds, before they mature, at the end of the investment horizon. Most of the literature that evaluates this strategy compares only ex post average returns or Sharpe ratios. In this paper, we use spanning tests to provide formal statistical evidence on the benefits of investing in long bonds when the investment horizon is short. The results for both the United States and Canada indicate that an investor with a short horizon is better off investing in short-term debt instruments than long-term bonds.     

Credit Risk Estimation for Small Businesses Based on a Statistical Method

Many financial statements are currently stored in databases, and statistical research of them can yield valuable results. We have developed a bankruptcy prediction model that determines fair interest rates for loans. Furthermore, we estimate the present discount values of loans with fair interest rates that depend on the quality of companies. If economic conditions are stable, it is possible to get stable returns with diversification of investment.     

Estimation of the bid - ask spread and its components: a new approach

We show that time variation in expected returns and/or partialprice adjustments lead to a downward bias in previous estimatorsof both the spread and its components. We introduce a new approachthat provides unbiased and efficient estimators of the componentsof the spread. We find that between 77 and 97 percent of thedownward bias in previous spread estimate is caused by timevariation in expected returns. More importantly, the adverse-selectioncomponent, though significant, accounts for a much smaller proportion(8 to 13 percent) of the quoted spread, at least for small trades,than the proportion (over 40 percent) previously reported inthe literature. Order processing costs are the predominant componentof quoted spreads.     

Bid-Ask Spread Estimation For A Correlated Value Innovation Process

Previous studies of bid-ask spread estimators based on serial covariance in returns document high proportions of positive serial covariances and therefore negative spread estimates. These findings may be due to the effects of time-variation in expected returns. Although purging the effects of time-varying expected returns yields more reasonable results, the bid-ask spread estimates from daily and weekly returns are still materially different. We present a method that avoids the need for removing the effects of time-varying expected returns by using a spread estimator developed directly for a correlated value innovation process. The new spread estimator not only yields more reasonable estimates of the bid-ask spread than the Roll (1984) model, but the spread estimates from daily and weekly returns are almost equal.     

Efficient estimation of lower and upper bounds for pricing higher-dimensional American arithmetic average options by approximating their payoff functions

In this paper, we develop an efficient payoff function approximation approach to estimating lower and upper bounds for pricing American arithmetic average options with a large number of underlying assets. The crucial step in the approach is to find a geometric mean which is more tractable than and highly correlated with a given arithmetic mean. Then the optimal exercise strategy for the resultant American geometric average option is used to obtain a low-biased estimator for the corresponding American arithmetic average option. This method is particularly efficient for asset prices modeled by jump-diffusion processes with deterministic volatilities because the geometric mean is always a one-dimensional Markov process regardless of the number of underlying assets and thus is free from the curse of dimensionality. Another appealing feature of our method is that it provides an extremely efficient way to obtain tight upper bounds with no nested simulation involved as opposed to some existing duality approaches. Various numerical examples with up to 50 underlying stocks suggest that our algorithm is able to produce computationally efficient results.     

The Impact of Investment Opportunities and Free Cash Flow on Financial Liberalization:A Cross-Firm Analysis of Emerging Economies

This study undertakes firm-level analysis of investment opportunities and free cash flow in an attempt to explain the source of the wealth effect of financial liberalization for 14 emerging countries. We find that the market's responses to stock market liberalization announcements are more favorable for high-growth firms than for low-growth firms, a result that is consistent with the investment opportunities hypothesis. We also demonstrate that firms with high cash flow experience lower announcement-period returns associated with stock market liberalization than do firms with low cash flow. Our findings suggest that the free cash flow hypothesis dominates the corporate governance hypothesis in terms of the net effect of stock market liberalization on a firm's stock returns. We further document similar evidence with regard to banking liberalization. Finally, we demonstrate that stock market liberalization leads to the more efficient allocation of capital.