### Glamour, Value And Anchoring On The Changing P/E

The York Management School

University of York (UK)

October 23, 2015

**Abstract: **

The fact that value shares outperform glamour shares in the long term has been known for over 50 years. Why then do glamour shares remain popular? The P/E ratio was the first statistic documented to discriminate between the two. Using data for all US stocks since 1983, we find that glamour shares have a much greater tendency to change P/E decile than value shares. We use TreeAge decision tree software, which has not been applied to problems in finance before, to show that glamour investors cannot rationally expect any windfall as their company’s P/E decile changes, whatever their horizon. We infer that glamour investors anchor on the initially high P/E value, underestimate the likelihood of change and are continually surprised. We also seek theoretical justification for why value shares tend to outperform glamour shares. No convincing arguments based on the efficient market hypothesis have been put forward to show that the outperformance of value shares might be due to their being fundamentally riskier. Here we apply equations from option theory to show that value shares can indeed be expected to outperform glamour shares.

### Glamour, Value And Anchoring On The Changing P/E – Introduction

It has been known since Nicholson (1960) that portfolios of low P/E ‘value’ shares give better returns in the long term than portfolios of high P/E ‘glamour’ shares. This poses a serious problem for those who believe that stock markets are mostly efficient. Attempts to find a theoretical justification for the observed outperformance of value shares have revolved around showing that these must somehow be riskier than glamour shares. However those attempts have to date failed to convincingly demonstrate a suitable risk factor. For example Lakonishok, Shleifer and Vishny (1994) concluded that value shares are not fundamentally riskier and indeed outperform in ‘bad’ states of the world.

Lakonishok, Shleifer and Vishny proposed one possible behavioural explanation: institutional investors may prefer glamour stocks because they want to appear more prudent. Having on average appreciated in price recently, glamour shares are easier to justify to sponsors. In this paper we propose a different behavioural explanation for the value/glamour split: the differing experiences of glamour and value investors can be explained by appealing to the fact of investors’ own bounded rationality. One well known feature of that bounded rationality is anchoring, where subjects are given an initial numerical estimate of a number, required to make an uncertain judgement of the true value and start off by adjusting their answer from that number. Investors may anchor on the P/E ratio currently attached to a stock when they invest in it. Having bought the stock, they expect the P/E to change slowly, if at all. As time goes on, the P/E decile changes, and different prospects for returns attach to each decile. If there is a differential drift in the P/E and hence returns between value and glamour stocks that is not expected by investors, this could account for why glamour investors end up disappointed. To date there has been some theoretical research into how P/Es change through time (e.g. Alcock, Mollee and Wood, 2011) but no investigation into the observed facts.

Our research objectives are therefore to address the following questions:

- Is there justification for the P/Es of value and glamour shares to change at different rates and the fact that value shares outperform glamour shares?
- What are the observed changes in P/Es and the returns that attach to them, and do investors’ decisions appear to be affected by anchoring? For this question we limit the calculations to one-year returns, hence:
- Can glamour shares’ returns match or exceed those of value shares over any time period?

We review the literature on explaining the so-called P/E anomaly and on the anchoring heuristic in behavioural finance in Section 2. Section 3 addresses research question 1 by describing the current state of knowledge of the P/E as a stochastic variable and looks at whether value and glamour shares’ expected prices and P/Es are likely to evolve differently. Sections 4 to 7 address research question 2: Section 4 describes our dataset and methodology, Section 5 presents and analyses our main results, Section 6 estimates the anchoring effect for glamour shares and Section 7 checks whether the results for the glamour decile depend on particular subsets of the data. Section 8 addresses research question 3 through multi-year Markov model simulations in TreeAge. Section 9 concludes and offers suggestions for further research.

The facts we establish are as follows. In respect of question 1, we find by applying option pricing theory and Merton’s model that prices, and thus P/Es, of value and glamour shares can indeed be expected to move differently. We show that for all plausible values of the parameters, the expected value share prices will grow more quickly than those of glamour shares. Moving on to question 2, we establish by analysing historical data that glamour shares give three times the returns of value shares if they stay in the same decile, but they have a much greater tendency to move decile. This results in the relative performances reversing, and the familiar value/glamour split, where value shares outperform glamour shares by about 7% p.a. Glamour investors appear to be under-estimating the tendency of their shares to change decile by at least 18%, and possibly much more. Smaller companies, and particularly the sort of small high-growth companies concentrated on AMEX / NYSE MKT, are much more likely to fall into losses, but the effect varies little through time. The Markov simulation allows us to tackle question 3 and shows unimpressive returns for glamour investors whatever their time horizon, but it does demonstrate the superior returns that value investors can expect if they hold for 2-3 years, as recommended by Ben Graham (Graham, 1976).

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