# 金融代写|利率理论代写portfolio theory代考|FORECASTING INDIVIDUAL SECURITY RETURNS

#### Doug I. Jones

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## 金融代写|利率理论代写portfolio theory代考|FORECASTING INDIVIDUAL SECURITY RETURNS

An individual security’s expected returns are almost always based on estimates provided by analysts. The techniques used for obtaining these forecasts are contained in Chapters 17, 18, and 19, which discuss valuation models, earnings estimation, and efficient markets. In this section, we discuss some characteristics of these forecasts that need to be taken into account when forming portfolios.

Researchers have found that forecasts of analysts across the stocks they follow tend to be too optimistic and too diverse, having too high a mean and too much dispersion. Nevertheless, researchers have found that analysts’ estimates do have information content [see, e.g., Elton, Gruber, and Grossman (1986)]. However, there is substantial error. A useful way to think about the information is that these are nuggets of gold in a large pile of rock. If this information is used directly as input into a portfolio optimizer, then the extreme estimates will result in a portfolio that includes very few securities, frequently heavily concentrated in only one or two. These heavily concentrated portfolios will have high risk. Given the substantial error in forecasts of expected return, the extra return from these portfolios is likely to be small, and given the higher risk, the portfolios are likely to perform poorly. The object then is to devise techniques that still utilize the information in the forecasts but result in well-diversified portfolios.

Diversification serves three purposes. First, diversified portfolios have lower risk than more concentrated portfolios selected from the set of diverse forecasts. Second, it is generally believed that analysts’ estimates have some information content but with lots of random noise. If the errors are uncorrelated, then a larger portfolio reduces the amount of random noise and increases the chance that the extra return is observed. Third, increasing the number of securities and reducing the amount invested in any single one reduces the amount invested in a security due to the extreme estimate of one analyst.

The easiest way to ensure diversification is to put upper limits on the amount invested in each security. A $2 \%$ upper limit will guarantee at least 50 securities in any given portfolio. A $1 \%$ limit would guarantee 100 securities. Upper limits are useful and are a common feature in most analysis. The difficulty is that many securities will be at the upper limit. If we believe securities with high forecasted expected returns are more desirable on average, then we would like to hold these securities in higher proportions. An upper limit of $1 \%$ to ensure at least 100 securities in the portfolio may be harmful if some of the securities with highest forecasted expected returns or desirable risk characteristics are securities in which we would like to invest more heavily. How else can one ensure reasonable diversification while allowing higher allocations to some securities?

One way to do this is to allow higher upper bounds but to process analysts’ data to reduce some of the extreme variability. The simplest way to make forecasts less extreme and avoid the difficulties caused by this is to move all the forecasts part way to the mean and adjust the whole distribution of analysts’ estimates so that it has a mean consistent with what we believe is appropriate for the type of securities being examined.

For example, if we employ analysts who forecast a $16 \%$ return for the average equity security and we forecast a market return of $12 \%$ for equities, we can first lower all analysts’ individual estimates by $4 \%^8$ Then, to get rid of the extreme forecasts, we can adjust all forecasts toward the mean. For example, if an analyst’s forecast is an expected return of $20 \%$ for stock ABC, we would first adjust the forecasts so all of the forecasts have a mean consistent with our beliefs or, in this case, reduce it by $4 \%$ to $16 \%$. Then we further adjust it by some percentage (e.g., $50 \%$ ) of the difference of the forecast from the forecasted mean. Thus the forecast would be $16-(1 / 2) 4=14$ for $\mathrm{ABC}$. This type of adjustment preserves the rank order of the forecasts and, by making them less extreme, results in a more diversified portfolio. The difficulty with this simple adjustment is that if one believes that the securities differ in risk, the simple adjustment does not preserve the rank order of what analysts believe are good purchases (e.g., an expected return more than commensurate with their risk).

## 金融代写|利率理论代写portfolio theory代考|PORTFOLIO ANALYSIS WITH DISCRETE DATA

Often analysts’ information about expected return comes in the form of discrete rankings rather than an estimate of expected return. For example, one common ranking used by industry is to place a stock in one of the following five categories:

3. hold
4. sell
5. strong sell
If this is the form of analyst information, then different techniques for forming portfolios are required.

The optimum way to utilize these data depends on how one believes the groups were formed in the first place. In most cases, the belief is that they were formed without any consideration of the risk characteristics of the securities. In this case, there is no single optimum method for utilizing these data. However, there are a number of methods that are sensible.

One technique that can be used is to construct an index fund out of the top group or groups. To construct an index fund, one would decide on the return-generating process that best fits the data (see Chapters 7 and 8 ) and then determine the sensitivities of the market to the factors in the model. Once these are determined, one would construct a portfolio from the top-ranked securities with the same sensitivity as the market to each of the factors and that has minimal residual risk. Such a portfolio has some nice characteristics. First, if the rankings contain no information, then one has constructed a portfolio that should mimic an index fund. Second, if there is information in the rankings, then the portfolio should have volatility similar to the market and be highly correlated with the market (move up and down with the market) but have extra return. In other words, such a portfolio would perform like an enhanced return index fund. The only condition under which the portfolio would not perform well is if the information in the rankings were perverse, that is, the highest-ranked securities were actually the worst securities to hold.

# 利率理论代考

## 金融代写|利率理论代写portfolio theory代考|PORTFOLIO ANALYSIS WITH DISCRETE DATA

1. 强买
2. 抓住
3. 强势卖出
如果这是分析师信息的形式，则需要不同的技术来形成投资组合。

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