\u210e \u210e \u210e FIN 300 Risk and Return Pt 1 18 Return vs Risk Any rational investor

ℎ ℎ ℎ fin 300 risk and return pt 1 18 return vs

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𝐸𝐴𝑝𝑝𝐴𝑝𝑖𝑝𝑖𝑅𝑦 𝑝𝑜 𝑅ℎ𝐴 𝑖 𝑡ℎ 𝐴𝐴𝑅𝑅𝐴𝑅 𝑅 𝑖 = 𝑖 𝑡ℎ 𝐴𝐴𝑅𝑅𝐴𝑅 FIN 300 - Risk and Return Pt. 1 18
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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
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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
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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
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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
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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
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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 !
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