Executive summary

The Capital Asset Pricing Model (CAPM) is considered a pivotal model in the computation of investment risk and the expected return on the investment. CAPM provides a way of ascertaining the expected return for stocks and estimating the required return. The single-index model (SIM) also aids in measuring the return and risk of a stock. It assumes that there is only one macroeconomic factor that brings about systematic risk influencing all stock returns. The APT model proposes that the return on financial security has a linear relationship with H systematic risk factors. The assertion made is that investors want to be given compensation for all of the risk factors that have a systematic impact on a security return. The Fama-French (FF) three-factor model divides the fundamental factors into three factors comprising the value factor, market factor, and scale factor for a more improved expounding influence of excess return. The models rationale is that firms with high value and small-capitalization repeatedly outperform the overall market. The Black-Scholes formula expresses the current value of a European call option on a stock that does not pay any dividends before the option's expiration. As computed, the call option is 11.06, whereas the put option is 3.93. As computed, the Sharpe ratio is 0.68, the Treynor Measure is 11.97, Jensen's Alpha is 2.05, and the information ratio is 0.098.

Table of contents

Introduction 4

CAPM and extensions 4

APT and extensions 6

Economic indicators and the business cycle 8

Option pricing 8

Forward and Futures pricing 10

Performance evaluation models 11

Recommendations 14

Conclusions 14

References 15

Introduction

Investment security analysis encompasses the valuation of certain securities that might be incorporated into the portfolio. This report conducts an extensive examination of investment and portfolio analysis. Specifically, the report will examine the capital asset pricing model, the single-index model, the arbitrage pricing theory, and the Fama-French three-factor models. Secondly, the report will discuss the Black-Scholes formula and compute call and put options. Also, considering the suitable performance measure relies on the portfolio's role to be assessed, the report will delve into the discussion of Sharpe ratio, information ratio, Treynor measure, and Jensen alpha.

CAPM and extensions

Irrespective of the extent to which investments are diversified, there is always some risk level that will be existent. Bearing this in mind, proper investment management necessitates seeking out a return...

The Capital Asset Pricing Model (CAPM) is a pivotal model in the computation of investment risk and the expected return on the investment. Any investment faces two types of risk, including the systematic risk and the unsystematic risk. On the one hand, systematic risk refers to market risks related to matters affecting the market, such as a financial recession. In contrast, unsystematic risk refers to the specific risk that is linked to individual stocks. CAPM is employed to examine this specific risk and uses the following formula:

In this case:

R? = Expected return to a stock

Rrf = the risk-free rate

Rm = the return to the market

? = Beta of the stock

(Rm - R rf ) = Equity market premium

The single-index model (SIM) is a relatively basic model for financial asset pricing that is largely employed in measuring the return and risk of a stock. In particular, the model for this particular model is delineated as follows:

In this case:

rit = return to a stock i in period t

rf = the risk-free investment return rate, for instance, interest rate from the United States Treasury Bills

rmt = the return to the market portfolio in period t

?i = the Alpha for the stock. This also refers to the abnormal return of the stock

?i = the beta for the stock....

…1.19

= 11.97

Jensen's Alpha

Jensen's Alpha is defined as the factor of return that facilitates the reconciliation of the actual returns to those forecasted by the CAPM. For the most part, Jensen's Alpha is employed as a metric of the risk-adjusted return generated by a portfolio. Imperatively, Michael Jensen came up with this CAPM extension as an approach for appraising fund managers (Feibel, 2003). Jensen's Alpha is computed using the following formula:

Jensens Alpha = (RPi RFi) [CAPM beta * (RMi Rfi)]

In the case of the fund portfolio

Jensens Alpha = (16% - 1.75%) [1.19 *(12% - 1.75%)]

= 14.25% - 12.20%

= 2.05

Information ratio

Information ratio is largely pertinent when evaluating a portfolio that is mixed with the benchmark portfolio. The following formula is employed:

Information Ratio = Alpha / Residual Standard Deviation

= 2.05 / 21

= 0.098

Morningstar Risk-Adjusted Return

Morningstar Risk-Adjusted Return is attuned for risk by computing a risk penalty for every investment's return based on the expected utility theory, a frequently applied economic examination approach. This concept supposes that investors are warier about conceivable poor results than unanticipated good results. These investors are also prepared to give a minimal percentage of the expected return of an investment in return for better certainty (Morningstar, 2020). This idea is the foundation of how Morningstar adjusts for risk. A risk penalty is deducted from every investment's total return, based on the dissimilarity in its month-to-month return in the course of the rating period, with a focus on downward disparity. The greater the disparity, the greater the penalty. If the two funds have a precisely similar return, the fund with greater variation in its return is handed the greater risk penalty (Boccadoro, 2014).

Morningstar's Risk-Adjusted Return Measure = APR APRT-Bill Mrisk

= APR APRT-Bill (0.0111 * StDev2)

= 16% - 1.75 (0.00111 * (21%) 2)

= 0.1599

Conclusions

A…