𝐸𝐴𝑝𝑝𝐴𝑝𝑖𝑝𝑖𝑅𝑦 𝑝𝑜 𝑅ℎ𝐴 𝑖 𝑡ℎ 𝐴𝐴𝑅𝑅𝐴𝑅 𝑅 𝑖 = 𝑖 𝑡ℎ 𝐴𝐴𝑅𝑅𝐴𝑅 FIN 300 - Risk and Return Pt. 1 18
Return vs. Risk • Any rational investor would prefer investments with a higher return • However, there is a tradeoff • Generally speaking, investments offering a higher return also come with a higher level of risk • As investors, we have to balance the desire of more return vs. the concern of taking on more risk FIN 300 - Risk and Return Pt. 1 19
Return vs. Risk • If I desire the utmost in safety in an investment, I will put my money in an FDIC insured bank account or T-Bills – However, I would expect to get very little return • If I am aiming for a higher investment return, I might invest in the stock market – However, I would have to be willing to bear significantly more risk • Much of what we do in finance centers on how to make our investment choices and negotiate the tradeoff between risk and return FIN 300 - Risk and Return Pt. 1 20
Measuring Risk • In finance, we use statistical measures to measure risk and return • We use the concept of mean to describe the return • Now, we will use variance and standard deviation to measure the risk, or volatility, of investment returns FIN 300 - Risk and Return Pt. 1 21
Statistics Formulas 𝑀𝐴𝐴𝑅 = 𝜇 = 𝑅 � = 1 𝑁 � 𝑅 𝑖 𝑁 𝑖=1 𝑃𝐴𝐴𝑖𝐴𝑅𝑚𝐴 = 𝜎 2 = 1 𝑁−1 ∑ 𝑅 𝑖 − 𝑅 � 2 𝑁 𝑖=1 𝑆𝑅𝐴𝑅𝐸𝐴𝐴𝐸 𝐷𝐴𝐴𝑖𝐴𝑅𝑖𝑝𝑅 = 𝜎 = 𝜎 2 = 𝑃𝐴𝐴𝑖𝐴𝑅𝑚𝐴 The above formulas are known as the sample mean , sample variance , and sample standard deviation Also, these formulas assume the outcomes to be equally weighted We typically use such formulas to measure (actual observed) historical returns FIN 300 - Risk and Return Pt. 1 22 Returns are equally weighted
Standard Deviation and Variance with Probabilities • Let’s return to our previous example, where we calculated the expected (or, probability-weighted average) return • Now, let’s calculate the variance and standard deviation for that set of probable scenarios FIN 300 - Risk and Return Pt. 1 23
Standard Deviation w/Probabilities • Scenario 1: 20% probability earning a +20% return • Scenario 2: 30% probability earning a +5% return • Scenario 3: 50% probability of earning a -10% return Steps to obtain the standard deviation: 1) Calculate the expected (mean) return as we did before 2) For each scenario, subtract the mean from the scenario return (this gives us the “ deviation ” for each scenario) 3) For each scenario, square the deviation (this gives us the “ squared deviation ” for each scenario) 4) Now, calculate the probability-weighted average of the “squared deviations” (this gives us the variance) 5) Finally, take the square root to obtain the standard deviation !
- Fall '08
- Corporate Finance, Return Pt.