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会计代写|财务管理代写Financial Management代考|Risk Analysis in Investment Decisions
Most thoughtful individuals and some investment bankers know that all interesting financial decisions involve risk as well as return. By their nature, business investments require the expenditure of a known sum of money today in anticipation of uncertain future benefits. Consequently, if the discounted cash flow techniques discussed in the last chapter are to be useful in evaluating realistic investments, they must incorporate considerations of risk as well as return. Two such considerations are relevant. At an applied level, risk increases the difficulty of estimating relevant cash flows. More importantly at a conceptual level, risk itself enters as a fundamental determinant of investment value. If two investments promise the same expected return but have differing risks, most of us will prefer the low-risk alternative. In the jargon of economics, we are risk averse, and as a result, risk reduces investment value.
Risk aversion among individuals and corporations creates the common pattern of investment risk and return shown in Figure 8.1. The figure shows that for low-risk investments, such as government bonds, expected return is modest, but as risk increases, so too must the anticipated return. I say “must” because the risk-return pattern shown is more than wishful thinking. Unless higher-risk investments promise higher returns, you and I, as risk-averse investors, will not hold them.
This risk-return trade-off is fundamental to much of finance. Over the past five decades, researchers have demonstrated that under idealized conditions, and with risk defined in a specific way, the risk-return trade-off is a straightline one as depicted in the figure. The line is known as the market line and represents the combinations of risk and expected return one can anticipate in a properly functioning economy.
The details of the market line need not detain us here. What is important is the realization that knowledge of an investment’s expected return is not enough to determine its worth. Instead, investment evaluation is a twodimensional task involving a balancing of risk against return. The appropriate question when evaluating investment opportunities is not “What’s the rate of return?” but “Is the return sufficient to justify the risk?” The investments represented by $\mathrm{A}$ and $\mathrm{B}$ in Figure 8.1 illustrate this point. Investment A has a higher expected return than $\mathrm{B}$; nonetheless, $\mathrm{B}$ is the better investment. Despite its modest return, B lies above the market line, meaning it promises a higher expected return for its risk than available alternatives, whereas investment A lies below the market line, meaning alternative investments promising a higher expected return for the same risk are available. ${ }^1$
会计代写|财务管理代写Financial Management代考|Risk and Diversification
Dispersion risk, as just described, is often known as an investment’s total risk, or more fancifully its Robinson Crusoe risk. It is the risk an owner would face if he were alone on a desert island unable to buy any other assets. The story changes dramatically, however, once the owner is off the desert island and again able to hold a diversified portfolio. For then the risk from holding a given asset is customarily less than the asset’s total risk-frequently a lot less. In other words, there is more-or perhaps I should say less-to risk than simply dispersion in possible outcomes.
To illustrate why, Table 8.1 presents information about two very simple risky investments: the purchase of an ice cream stand and an umbrella shop. ${ }^3$ For simplicity, let’s suppose tomorrow’s weather will be either rain or sun with equal probability. Purchase of the ice cream stand is clearly a risky undertaking, because the investor stands to make a 60 percent return on his investment if it is sunny tomorrow but lose 20 percent if it rains. The umbrella shop is also risky, because the investor will lose 30 percent if tomorrow is sunny but will make 50 percent if it rains.
Yet despite the fact that these two investments are risky when viewed in isolation, they are not risky when seen as members of a portfolio containing both investments. In a portfolio consisting of half ownership of the ice cream stand and of the umbrella shop, the losses and gains from the two investments precisely counterbalance one another in each state, so that regardless of tomorrow’s weather, the outcome is a certain 15 percent (e.g., if it is sunny tomorrow, the ice cream stand makes 60 percent on half of the portfolio and the umbrella shop loses 30 percent on the other half for a net of 15 percent $[15 \%=0.5 \times 60 \%+0.5 \times-30 \%])$. The expected outcome from the portfolio is the average of the expected outcomes from each investment, but the risk of the portfolio is zero. Owning both assets eliminates the dispersion in possible returns. Despite what you may have heard, there really is a free lunch in finance. It is called diversification.
This is an extreme example, but it does illustrate an important fact about risk: When it is possible to own a diversified portfolio, the relevant risk is not the investment’s risk in isolation-its Robinson Crusoe risk- but its risk as part of the portfolio. And, as the example demonstrates, the difference between these two perspectives can be substantial.
An asset’s risk in isolation is greater than its risk as part of a portfolio whenever the asset’s returns and the portfolio’s returns are less than perfectly correlated. In this commonplace situation, some of the asset’s return variability is offset by variability in the portfolio’s returns, and the effective risk borne by the investor declines. Look again at Table 8.1. The return on the ice cream stand is highly variable, but because it hits a trough precisely when the umbrella shop return hits a peak, return variability for the two investments combined disappears. The portfolio will earn 15 percent rain or shine. In other words, when assets are combined in a portfolio, an “averaging out” process occurs that reduces risk.
财务管理代考
会计代写|财务管理代写Financial Management代考|Risk Analysis in Investment Decisions
大多数有思想的人和一些投资银行家都知道，所有有趣的财务决策都涉及风险和回报。就其性质而言，商业投资需要今天支出一笔已知的资金，以预测不确定的未来收益。因此，如果上一章讨论的贴现现金流量技术要对评估现实投资有用，它们必须结合风险和回报的考虑。两个这样的考虑是相关的。在应用层面，风险增加了估计相关现金流量的难度。更重要的是，在概念层面上，风险本身是投资价值的基本决定因素。如果两项投资承诺相同的预期回报但风险不同，我们大多数人会更喜欢低风险的选择。用经济学的术语来说，
个人和公司之间的风险规避创造了图 8.1 所示的投资风险和回报的共同模式。该图显示，对于政府债券等低风险投资，预期回报率适中，但随着风险增加，预期回报率也必须增加。我说“必须”是因为所显示的风险回报模式不仅仅是一厢情愿的想法。除非更高风险的投资承诺更高的回报，否则作为规避风险的投资者，你我不会持有它们。
这种风险回报权衡是大部分金融的基础。在过去的五年中，研究人员已经证明，在理想化条件下，并且以特定方式定义风险时，风险与回报的权衡是一条直线，如图所示。这条线被称为市场线，代表了在正常运行的经济中可以预期的风险和预期回报的组合。
市场线的细节不必在这里停留。重要的是认识到投资的预期回报不足以决定其价值。相反，投资评估是一项涉及风险与回报平衡的二维任务。评估投资机会时，适当的问题不是“回报率是多少？” 但是“回报是否足以抵消风险？” 代表的投资A和乙在图 8.1 中说明了这一点。投资 A 的预期回报高于乙; 尽管如此，乙是更好的投资。尽管回报不大，但 B 位于市场线上方，这意味着它承诺其风险的预期回报高于可用替代方案，而投资 A 位于市场线下方，这意味着可以使用承诺在相同风险下获得更高预期回报的替代投资。1
会计代写|财务管理代写Financial Management代考|Risk and Diversification
正如刚才所描述的，分散风险通常被称为投资的总风险，或者更奇特的是它的鲁滨逊漂流记风险。如果所有者独自一人在荒岛上无法购买任何其他资产，就会面临这种风险。然而，一旦所有者离开荒岛并再次能够持有多元化的投资组合，情况就会发生巨大变化。因为持有给定资产的风险通常小于该资产的总风险——通常要低得多。换句话说，与可能结果的简单分散相比，存在更多——或者我应该说更少——的风险。
为说明原因，表 8.1 提供了有关两项非常简单的风险投资的信息：购买冰淇淋摊和雨伞店。3为简单起见，我们假设明天的天气是下雨或晴天的概率相同。购买冰淇淋摊显然是一项冒险的事业，因为如果明天是晴天，投资者将获得 60% 的投资回报，但如果下雨，则损失 20%。雨伞店也有风险，因为如果明天是晴天，投资者将损失 30%，如果下雨，则将赚取 50%。
然而，尽管这两项投资在孤立的情况下是有风险的，但当它们被视为包含这两项投资的投资组合的成员时却没有风险。在由冰淇淋摊和雨伞店的一半所有权组成的投资组合中，两项投资的损失和收益在每个州都恰好相互抵消，因此无论明天的天气如何，结果都是确定的 15%（例如，如果明天是晴天，冰淇淋摊赚取一半投资组合的 60%，而雨伞店则损失另一半投资组合的 30%，净利润为 15%[15%=0.5×60%+0.5×−30%]). 投资组合的预期结果是每项投资预期结果的平均值，但投资组合的风险为零。拥有这两种资产消除了可能回报的分散。尽管您可能听说过，金融界确实有免费午餐。这叫做多元化。
这是一个极端的例子，但它确实说明了一个关于风险的重要事实：当有可能拥有多元化投资组合时，相关风险不是孤立的投资风险——鲁滨逊漂流记风险——而是作为投资组合一部分的风险. 而且，如示例所示，这两种观点之间的差异可能很大。
只要资产的回报和投资组合的回报不完全相关，资产的孤立风险就大于其作为投资组合的一部分的风险。在这种普遍情况下，部分资产回报的可变性被投资组合回报的可变性所抵消，投资者承担的有效风险下降。再看看表 8.1。冰淇淋摊的回报变化很大，但由于它恰好在雨伞店的回报达到顶峰时触及低谷，因此两项投资组合的回报可变性消失了。该投资组合将获得 15% 的风雨无阻收益。换句话说，当资产组合在一个投资组合中时，会发生降低风险的“平均化”过程。
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