Thursday, April 26, 2012 / ARM Research

The concept of matching return with risk in evaluating investment opportunities is widely and firmly established in finance, with Markowitz’s (1952) seminal paper providing the theoretical foundations for much of the work in this area. Since then, at least, volatility--measured as the standard deviation of (usually daily) returns--has become the most widely accepted measure of risk for financial assets, and the cornerstone of many asset allocation policies. Consequently, asset classes have been widely evaluated on the basis of their volatility and portfolio construction has formally rested on a mean-variance (or just variance) optimization framework despite its many known drawbacks. However, it is also true that volatility as a measure of risk is imperfect, often failing to reflect phenomena that are important to real life investors or even the empirical behaviour of assets. For instance, standard deviation as a measure of risk fails to capture the asymmetric quality of investor risk preferences (as Markowitz and many others after him point out). 

Another aspect that has received rather less press is risk as a measure of potential welfare loss over a given investment horizon. This redefinition of risk is particularly important in investments linked with life cycle goals, with their typical long term horizon and potentially dire consequences of failure for the investor. In this regard, a widely studied but still hugely under-appreciated phenomenon is the role of time in optimal investment decision making. The concept of time as arguably an investor’s greatest asset is hardly controversial. However, it has fared poorly in finding its way into formal asset allocation practices beyond heuristic application, even though techniques such as the increasingly popular life-cycle investing rely heavily on this concept.   
 

To demonstrate the potential impact of time on investment decisions we explore its effect on holding period returns (HPR) for Nigerian equities. The choice of equities is important because the effects of time on the characteristics of this asset class are easily demonstrable and have far reaching implications for asset allocation practices of institutional and other long term investors, among whom many common mis-characterisations of risk in this asset class (in this context) is no doubt leading to widespread adoption of sub-optimal portfolios.

In this paper, we see that time alters risk characteristics (in the traditional sense) of equities listed on the Nigerian Stock Exchange using 27 years of monthly data and making simple assumptions.  Similar studies have been replicated across various markets and asset classes—this report merely buttresses the (near) universality of this concept.  The many implications of these findings will be explored in subsequent papers.

To proceed, we examine the distribution of annualized returns of the NSE All Share Index (NSEASI) over several holding periods (3, 5, 7 and 10 years) based on monthly returns on the index. In essence, we wish to study the distribution of the potential outcomes for an investor who adopts a buy and hold strategy for the NSEASI[1] over the specified holding period (say 7 years) having randomly purchased this holding at the beginning of any given month during the last 27 years (allowing for the holding period of course).

The chart below shows the distribution of annualized nominal returns over corresponding rolling HPRs covering the period between Jan. 1985 and the end of Q1 2012 in histograms.

Figure 1: Annualised Holding Period Returns

   

      

Different strokes

The patterns in Figure 1 provide rich material for analysis and conclusions, but we focus for now on the most pertinent. First, it is clear that equity returns on the NSE have significant positive skews (i.e. much more likely to produce positive than negative returns) and fairly heavy tails (higher than normal[2] tendency for large gains and losses) over the various holding periods, consistent with patterns for multi-period for equity returns across the globe. The history provided by the NSE is quite astonishing however, reflecting a substantial probability for compounded nominal returns higher than 40% per annum in all cases. 

The more pertinent observations for our purposes nevertheless lie in the changes that occur in the distribution with the extension of the holding period. It is clear from the charts that the three year HPRs have the greatest potential for outsize positive returns, but they also carry substantial risk of loss, and significant ones at that. However, this risk reduces rapidly with holding period, and is non-existent (at least based on the history of the NSE) over a 10 year horizon. Perhaps more importantly, extending the holding period significantly reduces volatility of annualised returns. An explanation for this trend (also supported in literature) may lie in the fact that a longer investment tenors allows for an evening out of the troughs and peaks of the market cycles – reflecting both mean reversion and the law of large numbers.

Significantly, longer holding periods have much better risk adjusted return characteristics, which vary roughly linearly with time in the case of the NSEASI. For instance, Sharpe ratio for annualized 10 year returns is almost thrice the corresponding three year. Nor is this phenomenon unique to Nigeria; global equity indices exhibit increasing risk adjusted returns with investment horizon (see Figure 2)

Table 1: Summary Statistics for Compounded Annual Returns

Figure 2: Risk adjusted returns on the S&P 500[3] and STOXX 600

The immediate conclusion from this analysis is that Nigerian listed equities have markedly different risk/return characteristics over different holding periods, allowing for the imperfections in the measures adopted in this survey[4]. In addition, the more positive skews in longer holding periods does offer investors opportunities to meet long term goals which suggests that failure to incorporate the time dimension in asset allocation decisions could lead to substantial inefficiencies in portfolio construction. However the more pertinent conclusions will come from a comparative analysis of real (i.e. inflation adjusted) returns for equities vis-à-vis money market securities—which were the only market alternatives available to Nigeria oriented investors over the time period surveyed which will be the subject of a subsequent paper.  

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