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2 Valuation methods for individual investments Some of the methods used are market value, smoothed market value, fair value, discounted cashflow, stochastic models, arbitrage value, historic book value, written up and written down book value. 2.1 Market value The market value of an asset varies constantly and can only be known with certainty at the date a transaction in the asset takes place. Even in an open market more than one figure may be quoted at any time. However, for many traded securities it is an objective and easily obtained figure and is a starting point for asset valuation. Quoted securities generally have the following prices the bid price at which market makers are prepared to buy, the slightly higher offer price at which market makers are prepared to sell, the midmarket value an average of the bid and offer prices. Arguably, the bid price should instead be used for some purposes eg assessing the realisable value of a portfolio, possibly with allowance for sale costs. Market values are generally fairly easily available, objective, well understood. Question Suggest reasons why someone selling an asset may not obtain its market value. Solution An investor may not obtain the market value because market value may mean midmarket value rather than bid value, market value may mean yesterdays market value, net proceeds from a sale will be reduced by dealing costs and possibly tax, if they sell a large holding of an asset they may depress the price of the asset, if they own a strategic block of shares, they might receive more than the market value from a predator wishing to gain control of the company. End of question There are several possible problems that may arise when using market value Volatilitymarket values may be subject to wide fluctuations in the short term, which may not reflect changes in the expected future proceeds from the assets. Consequently, there may be quite different results from a valuation depending on the exact date. Achieving consistency the volatility of market values makes it difficult to value liabilities in a consistent manner, unless they are very closely matched, in which case their value will vary correspondingly. No quoted price in general, determining market value for quoted securities is relatively straightforward. This is not so true for unquoted investments such as direct property investment and venture capital holdings. Nevertheless, the vast majority of assets held by most funds for which actuaries have to perform valuations have clearly identifiable market values. 2.2 Smoothed market value Where market values are available, they can be smoothed by taking some form of average over a specified period to remove daily fluctuations. There are many different ways of obtaining a smoothed market value. One way is to use a moving average, so that the value of an asset on any particular day is taken as the average of the market price over, say, the previous three months. This method does not lend itself to consistent liability valuations because the appropriate discount rate for the liability valuation is indeterminate and requires judgement. There may be judgement, for example, in the length of the smoothing period, whether the average should be a simple average or a weighted average, with more weight on recent values. In practice the assessment becomes a view as to whether the asset is cheap or expensive in relation to its smoothed market value. 2.3 Fair value In recent years, there has been a move towards marketbased methods of valuation. Fair value is a concept developed by The International Accounting Standards Board IASB and is a marketbased method of valuation used for financial reporting. In accounting terms, fair value is the amount for which an asset could be exchanged or a liability settled between knowledgeable, willing parties at arms length. This definition does not specify how such a value is calculated. For most assets, in most market conditions, the fair value will simply be the market price. If the market price of an asset is not readily available, eg because the asset is not frequently traded, then a proxy might be sought in the form of an alternative fair value. There are various options available for calculating a fair value, for example seek an indicative price from a broker or market maker, use the most recent known price and adjust in line with the movement in an appropriate index, use a stochastic asset model to determine a marketconsistent value. Determining the fair value of liabilities is discussed in more detail in a later chapter. 2.4 Discounted cashflow This method involves discounting the expected future cashflows from an investment using longterm assumptions. The discounted cashflow also called discounted proceeds approach thus values an asset as the present value of the expected income stream and capital from the assets. Examples of this approach, which we discuss later in this chapter, include the discounted dividend model for equities, the discounted rental income approach to valuing property. This method has the advantage of being easily made consistent with the basis used to value an investors liabilities. The method used will be consistent if the assets and liabilities are valued on a discounted cashflow basis using the same approach to determine the discount rate. This consistency is fundamentally important. Where a portfolio of assets is held, a weighted discount rate can be calculated reflecting the proportions in each asset class, and this weighted discount rate can be used to value the liabilities. However, it relies on the assessment of a suitable discount rate, which is straightforward where the assets are, for example, highquality fixedinterest stocks but is less so otherwise. Where an investment has some adverse feature eg default risk or poor marketability it is usual to increase the rate of interest used to discount the cashflows. In this way a lower value is placed on more risky investments. 2.5 Stochastic models These are an extension of the discounted cashflow method in which the future cashflows, interest rates or both are treated as random variables. The result of a stochastic valuation is a distribution of values from which the expected value and other statistics can be determined. This method is particularly appropriate in complicated cases where future cashflows are dependent on the exercise of embedded options, such as the option to wind up in adverse financial circumstances. The advantages of a stochastic approach are it is good for valuing derivatives, it gives a better picture of a valuation, eg by giving a distribution of results, consistency with the liability valuation is also achievable. The disadvantages are that it may be too complex for many applications, the results are dependent on the assumed distributions for the variables these assumptions may be highly subjective. 2.6 Arbitrage value Arbitrage value is a means of obtaining a proxy market value and is calculated by replicating the investment with a combination of other investments and applying the condition that in an efficient market the values must be equal. The technique is often used in the valuation of derivatives. In other markets the technique is difficult or impossible to apply because it is difficult to replicate many assets. The use of arbitrage value to value futures and options is considered later in this chapter. 2.7 Historic book value This is the price originally paid for the asset and is often used for fixed assets in published accounts. In its favour, this method is objective, conservative but only if the value has risen since purchase, well understood, used for some accounting purposes. But for most valuation purposes, book value has little merit, since it is historical. 2.8 Written up or written down book value Written up or written down book value is historic book value adjusted periodically for movements in value. For example, a property investment may be revalued, say every three years. The current market value or the discounted cashflow value may influence the adjustment. But the adjusted book value may still not equal the market value. Arguably, the method is no more sensible than book value. Unlike book value, the method may be subjective. Neither of these book value based methods lends itself to the use of a consistent liability valuation because the appropriate discount rate for the liability valuation cannot be determined. Remember that if we are looking at the relationship between assets and liabilities, such as in a pension scheme valuation, we need to use a consistent valuation basis for both.