# Maths and Finance

Q#1. Rational investors should not invest their entire money in a single stock regardless of how highly-recommended that stock is by professional financial analysts. Investors are better off investing their money in a diversified manner to cut down investment risk and achieve a better risk-return tradeoff. Explain whether this makes financial sense and state your financial arguments for or against diversification. Also, state what percentage of the overall risk (SD) of a NYSE-listed average stock can be eliminated through diversification according to your book and what risk component is reduced via diversification. Limit your answers to ten sentences.

Q#2. If investors become more jittery (more risk-averse) about investing in the stock markets based on fears of prolonged US-China trade war, slower growth in the world economies, or other factors that could raise market risk, then what will happen to current stock prices and expected stock returns according to the predictions of the Capital Asset Pricing Model (CAPM)? Also, some may describe CAPM in a simple, non-technical way that it rewards investors for “waiting and worrying about their investments”. Discuss what CAPM variables may correspond to the waiting and worrying part of your invested money. Limit your answers to fifteen sentences.

Q#3. If you invest your entire capital in a financial sector mutual fund or exchange traded fund (ETF) with 50 financial stocks in each fund, then you would have eliminated all of the company-specific (unsystematic) risks and your portfolio will be almost fully diversified. Explain whether or not this is a valid diversification argument according to the discussion in Chapters 6 and 25. Limit your answers to ten sentences.

Q#4. Chapter 25 explains that it is better for investors to have some money invested in a risk-free asset and the remaining money in a stock market portfolio or stock-bond portfolio. A risk-free asset by definition will protect your initial investment (no default risk) even though it may not provide any return. Although we often use T-bill return as a risk-free return, your FDIC-insured checking/saving accounts may be regarded as a risk-free asset up to the FDIC protection limit. Remember that the return to risk ratio from the new efficiency frontier with the risk-free asset (i.e., CML) is better than from the old efficiency frontier with no risk-free asset (see figures 25-2 and 25-5). Explain why the addition of a risk-free asset will lower the overall portfolio risk and raise return to risk ratio. You may want to look at the two-asset portfolio return and variance formulas where one asset is a risk-free asset and other asset is a stock market portfolio. Limit your answers to ten sentences.

Last Updated on February 20, 2019

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