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Initial Return is the product of a collaboration between finance professionals, academics, and investors. We produce high-quality, educational content for investors, traders, and finance students.
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What is the risk-free rate?
The risk-free rate is the rate of return earned on a risk-free asset. While returns on risky assets such as stocks are uncertain, the key distinction of the risk-free rate of return is that we know its exact value at the time of investment. For example, we may expect a stock to yield 8% over…
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Return volatility formula and calculator
We start this lesson by discussing what is meant by (stock) return volatility. Then, we explain the return volatility formula. Finally, a simple return volatility calculator is provided for your convenience. What is (stock) return volatility? Imagine an investor who bought shares of a stock three years ago. According to the investor’s calculations, her annual…
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Arithmetic average return calculator and formula
In this lesson, we introduce a simple yet really useful measure of investment performance. In particular, we discuss the arithmetic average return formula and provide a practical arithmetic average return calculator. It is really important for investors to be able to accurately assess the performance of their investments. In that sense, arithmetic average (or mean)…
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Geometric average return calculator and formula
In this post, we explain the geometric average return formula using numerical examples and discuss how it differs from the arithmetic average return. We provide a practical geometric average return calculator as well. Geometric average return formula The geometric average return formula (or the geometric mean return formula) can be written as follows: While the…
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What is risk pooling?
Risk pooling is an important concept that is particularly relevant for areas such as finance, insurance, supply chain management, and healthcare. In this post, we offer a definition of risk pooling, provide examples, and discuss the relevance of risk pooling in different areas. We draw a distinction between risk pooling and risk sharing as well.…
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Risk aversion coefficient – meaning and formula
When we discussed investors’ risk preferences, we distinguished between risk-averse, risk-neutral, and risk-seeking behavior. We also explained that risk-averse investors expect compensation for bearing risk, which is called a risk premium. But, how do measure risk aversion? The answer is the risk aversion coefficient. It quantifies the degree to which an individual dislikes risk. In…
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What is liquidity in stocks?
Liquidity is a fundamental concept in finance and trading. But, what is liquidity in stocks in particular and financial markets in general? A liquid stock can be traded easily in relatively large volumes without affecting its price in the market. In contrast, illiquid stocks are traded thinly, such that it may be difficult to find…
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Jensen’s alpha formula and calculator
Jensen’s alpha is a popular performance evaluation metric, which was developed by the American financial economist Michael Jensen in the late 60s. It is a risk-adjusted performance measure (other examples include the Sharpe ratio and Treynor ratio) and is theoretically linked to the capital asset pricing model (or the CAPM). Jensen’s alpha formula We can…
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Fungible tokens – meaning and examples
Fungible tokens are one of the two main types of digital tokens, the other type being non-fungible tokens (NFTs). In this post, we explain in detail what fungible tokens are and how they differ from NFTs. Jump to: What is fungibility? Fungibility is all about interchangeability. Fiat money (US dollars, British pounds, Euro, etc.) is…
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NFT meaning, marketplaces, and scams
In this post, we offer a beginner’s guide to NFTs. We explain the meaning of an NFT and how NFTs are be traded in marketplaces. We also discuss various types of NFT scams. Jump to: What does NFT mean? NFT is an acronym for the term non-fungible token, a form of digital token. Most of…
Step-by-step tutorials:
Downloading stock price data
Plotting stock prices and returns
Creating a histogram of stock returns
Descriptive statistics for stock returns
Computing the correlation between two stocks
Calculating a stock’s beta
Modern portfolio theory:
Portfolio return
Portfolio risk
Efficient frontier
Optimal risky portfolio
Market equilibrium:
Capital asset pricing model (CAPM)
Arbitrage pricing theory (APT)
