FIN 366: I Chapter 5: Risk, Return, and the Historical Record

FIN 366: INVESTMENTS BRIEFING Chapter 5: Risk, Return, and the Historical Record Holding period returns (HPR) represent the capital gain (or price appreciation) and dividend yield (or income component) associated with a security over a period. Over multiple periods, we may average HPRs using the simple arithmetic average, or the geometric average which takes into account the time value of money. For returns less than one year, we annualize to express as a “return per year” using the Annual Percentage Rate (APR) by multiplying the per period rate by the number of periods per year, or by the Effective Annual Rate, which accounts for the compound growth from period to period. Risk considers a security or portfolio’s likelihood of achieving various returns. Scenario analysis helps to quantify risk by examining different possible returns in various economies or states of the world. The expected return is the “average” HPR an investor might expect from a security. The variance and standard deviation of the security’s returns quantify the risk associated with an investment, and the standard deviation is particularly useful because it is expressed in the same units as the returns, in percent. The risk premium is the expected return of a security above the risk-free rate (T-bills). The excess return is the actual return above the risk-free rate. Risk aversion implies investors demand a higher reward to invest in riskier assets. The Sharpe Ratio is a measure that provides the reward per “unit” of risk, or a way to compare returns from different portfolios while accounting for their risk levels. Capital Allocation is the choice between holding risky assets (stocks and bonds) and risk-free securities, and the complete portfolio consists of your holdings overall, risky and risk-free. The Capital Allocation Line is a graphical depiction of all different portfolio combinations achieved by adjusting our weights in risky vs. risk-free assets. The Capital Market Line is a version of the capital allocation line where the risky asset we use is the “market portfolio”, proxied by a market index mutual fund. Finally, nominal interest rates are the rates at which dollar values grow, while real interest rates capture the change in purchasing power by subtracting out inflation. .

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Optimal Life Extension Management of Offshore Wind Farms Based on the Modern Portfolio Theory
Article Optimal Life Extension Management of Offshore Wind Farms Based on the Modern Portfolio Theory Baran Yeter and Yordan Garbatov * Centre for Marine Technology and Ocean Engineering (CENTEC), Instituto Superior Técnico, University of Lisbon, 1049-001 Lisbon, Portugal; [email protected] * Correspondence: [email protected] Abstract: The present study aims to develop a risk-based approach to finding optimal solutions for life extension management for offshore wind farms based on Markowitz’s modern portfolio theory, adapted from finance. The developed risk-based approach assumes that the offshore wind turbines (OWT) can be considered as cash-producing tangible assets providing a positive return from the initial investment (capital) with a given risk attaining the targeted (expected) return. In this regard, the present study performs a techno-economic life extension analysis within the scope of the multi-objective optimisation problem. The first objective is to maximise the return from the overall wind assets and the second objective is to minimise the risk associated with obtaining the return. In formulating the multi-dimensional optimisation problem, the life extension assessment considers the results of a detailed structural integrity analysis, a free-cash-flow analysis, the probability of project failure, and local and global economic constraints. Further, the risk is identified as the variance from the expected mean of return on investment. The risk–return diagram is utilised to classify the OWTs of different classes using an unsupervised machine learning algorithm. The optimal portfolios for the various required rates of return are recommended for different stages of life extension. Citation: Yeter, B.; Garbatov, Y.
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Capital Asset Pricing Model
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