- Centre for Decision Research
This article is based on the authors’ publication Capital Gains Overhang with a Dynamic Reference Point, published in Management Science. https://doi.org/10.1287/mnsc.2019.3404.
Imagine you are used to buying a product for £10 every week. Now imagine that the price suddenly drops to £8. When you make your regular purchase that week, you will feel like you are making a £2 gain relative to the usual price of £10, because this price has become a reference point for you. If the price of the product subsequently stays at £8 for a prolonged period then you may eventually adjust your reference point down towards £8 and you would then be disappointed if the price rises back to £10, as £8 will be your new reference point.
Reference points mark the boundary of indifference between the perception of a gain versus a loss. As well as being used by general consumers, they are also relevant in the share market. If you recently bought a share for a price of £5 per share then you might regard a price move above £5 as a gain, or a price below £5 as a loss. This is because you are using the initial purchase price of £5 as a reference point.
In our paper, Capital Gains Overhang with a Dynamic Reference Point, we investigate other potential investor reference points. Aside from the purchase price, the next most important reference point that we identify is a prior high. For example, imagine that your share went up to a price of £8 and then declined back to £5. You may now feel that you are making a loss on the investment, as you could have sold out at the higher price of £8, rather than the current £5. In this instance, you are using a prior high as a reference point rather than the purchase price of £5.
We carried out an experiment to test how investors form reference points, by showing them a number of prior share price movements and then eliciting their reference point. We then investigated the relationship between the reference point and key prices in the share price path to generate a formula for the reference point. Our results suggest that multiple prior prominent prices are considered by investors when forming the reference point. We then generated formulas for the reference point that use a composite of these prices.
Reference points should be of interest to investors, as they have an effect on share prices. When shares are priced above the reference point, investors regard themselves as being in a position of gain. For this reason, they are more inclined to sell the shares, which leaves these shares under-priced and hence likely to outperform in the future. Equally, shares that are below the reference point induce a feeling of loss in investors. They are reluctant to sell these shares until the share price reaches the reference point, which leaves these shares overpriced and therefore likely to underperform in the future.
This raises the question of how we can identify the reference point for a share traded in the market, which has multiple investors? Investors can buy a share on any particular day which means that each investor would have a unique reference point that was different from the other investors. In order to determine the aggregate reference point for a share traded in the market, we used the Capital Gains Overhang (CGO) model to calculate the aggregate reference point across investors in a stock.
The CGO model uses the volume (shares traded) on a particular day to calculate the likely aggregate reference point for each share. If a particular day has a high volume then the prominent prices available on that day will be granted a greater weight within the calculation of the aggregate reference point.
Once we had established the formulas to calculate the likely reference point for a single investor, and found a model that was able to calculate an aggregate reference point across investors, we then undertook market testing to differentiate between under and over-priced stocks. We found that the composite reference points, formed from our earlier experiment, are better able to distinguish between stocks that are currently priced above their reference point (undervalued) and stocks that are currently priced below their reference point (overvalued).
Our composite reference points are more accurate than using the purchase price alone as the reference point, which is the assumption that much of the previous research literature has used. We also found that our composite reference points are better able to explain future trading volume than the purchase price alone.
Our findings have implications for investors in the share market. Our results suggest that shares may be under or over-priced due to the impact of the aggregate reference point, which leads to irrational decision-making on the part of investors. To avoid being overcome by this bias, investors should evaluate their current investments based on future potential alone and not allow their purchase price, or past key prices such as prior highs, to influence their investment decisions. In particular, investors should be willing to make the tough call to sell an investment that is making a loss relative to their purchase price or a prior attained high, if the future prospects for the share are poor.
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