Systematic Risk Archives

Specific risk

April 1, 2022 by Youssef LOURAOUI

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) explains the specific risk of financial assets, a key concept in asset pricing models and asset management in practice.

This article is structured as follows: we start with a reminder of portfolio theory and the central concept of risk in financial markets. We then introduce the concept of specific risk of an individual asset and especially its sources. We then detail the mathematical foundation of risk. We finish with an insight of the relationship between diversification and risk reduction with a practical example to test this concept.

Portfolio Theory and Risk

Markowitz (1952) and Sharpe (1964) created a framework for risk analysis based on their seminal contributions to portfolio theory and capital market theory. All rational profit-maximizing investors attempt to accumulate a diversified portfolio of risky assets and borrow or lend to achieve a risk level consistent with their risk preferences given a set of assumptions. They established that the key risk indicator for an individual asset in these circumstances is its correlation with the market portfolio (the beta).

The variance of returns of an individual asset can be decomposed as the sum of systematic risk and specific risk. Systematic risk refers to the proportion of the asset return variance that can be attributed to the variability of the whole market. Specific risk refers to the proportion of the asset return variance that is unconnected to the market and reflects the unique nature of the asset. Specific risk is often regarded as insignificant or irrelevant because it can be eliminated in a well-diversified portfolio.

Sources of specific risk

Specific risk can find its origin in business risk (in the assets side of the balance sheet) and financial risk (in the liabilities side of the balance sheet):

Business risk

Internal or external issues might jeopardize a business. Internal risk is directly proportional to a business’s operational efficiency. An internal risk would include management neglecting to patent a new product, so eroding the company’s competitive advantage.

Financial risk

This pertains to the capital structure of a business. To continue growing and meeting financial obligations, a business must maintain an ideal debt-to-equity ratio.

Mathematical foundations

Following the Capital Asset Pricing Model (CAPM), the return on asset i, denoted by R_i can be decomposed as

img_SimTrade_return_decomposition

Where:

R_i the return of asset i
E(R_i) the risk premium of asset i
β_i the measure of the risk of asset i
R_M the return of the market
E(R_M) the risk premium of the market
R_M – E(R_M) the market factor
ε_i represent the specific part of the return of asset i

The three components of the decomposition are the expected return, the market factor and an idiosyncratic component related to asset only. As the expected return is known over the period, there are only two sources of risk: systematic risk (related to the market factor) and specific risk (related to the idiosyncratic component).

The beta of the asset with the market is computed as:

Beta

Where:

σ_i,m : the covariance of the asset return with the market return
σ_m² : the variance of market return

The total risk of the asset measured by the variance of asset returns can be computed as:

Decomposition of total risk

Where:

β_i² * σ_m² = systematic risk
σ_εi² = specific risk

In this decomposition of the total variance, the first component corresponds to the systematic risk and the second component to the specific risk.

Decomposition of returns

We analyze the decomposition of returns on Apple stocks. Figure 1 gives for every month of 2021 the decomposition of Apple stock returns into three parts: expected return, market factor (systematic return) and an idiosyncratic component (specific return). We used historical price downloaded from the Bloomberg terminal for the period 1999-2022.

Figure 1. Decomposition of Apple stock returns:
expected return, systematic return and specific return.
Decomposition of asset returns Computation by the author (data: Bloomberg).

You can download below the Excel file which illustrates the decomposition of returns on Apple stocks.

Why should I be interested in this post?

Investors will be less influenced by single incidents if they possess a range of firm stocks across several industries, as well as other types of assets in a number of asset classes, such as bonds and stocks.

An investor who only bought telecommunication equities, for example, would be exposed to a high amount of unsystematic risk (also known as idiosyncratic risk). A concentrated portfolio can have an impact on its performance. This investor would spread out telecommunication-specific risks by adding uncorrelated positions to their portfolio, such as firms outside of the telecommunication market.

Useful resources

Academic research

Evans, J.L., Archer, S.H. 1968. Diversification and the Reduction of Dispersion: An Empirical Analysis. The Journal of Finance, 23(5): 761–767.

Markowitz, H. 1952. Portfolio Selection. The Journal of Finance, 7(1): 77-91.

Mossin, J. 1966. Equilibrium in a Capital Asset Market. Econometrica, 34(4): 768-783.

Sharpe, W.F. 1963. A Simplified Model for Portfolio Analysis. Management Science, 9(2): 277-293.

Sharpe, W.F. 1964. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, 19(3): 425-442.

Tole T.M. 1982. You can’t diversify without diversifying. The Journal of Portfolio Management. Jan 1982, 8 (2) 5-11.

About the author

The article was written in April 2022 by Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022).

Systematic risk

April 1, 2022 by Youssef LOURAOUI

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) presents the systematic risk of financial assets, a key concept in asset pricing models and investment management theories more generally.

This article is structured as follows: we introduce the concept of systematic risk. We then explain the mathematical foundation of this concept. We present an economic understanding of market risk on recent events.

Portfolio Theory and Risk

Markowitz (1952) and Sharpe (1964) developed a framework on risk based on their significant work in portfolio theory and capital market theory. All rational profit-maximizing investors seek to possess a diversified portfolio of risky assets, and they borrow or lend to get to a risk level that is compatible with their risk preferences under a set of assumptions. They demonstrated that the key risk measure for an individual asset is its covariance with the market portfolio under these circumstances (the beta).

The fraction of an individual asset’s total variance attributable to the variability of the total market portfolio is referred to as systematic risk, which is assessed by the asset’s covariance with the market portfolio. Systematic risk can be decomposed into the following categories:

Interest rate risk

We are aware that central banks, such as the Federal Reserve, periodically adjust their policy rates in order to boost or decrease the rate of money in circulation in the economy. This has an effect on the interest rates in the economy. When the central bank reduces interest rates, the money supply expands, allowing companies to borrow more and expand, and when the policy rate is raised, the reverse occurs. Because this is cyclical in nature, it cannot be diversified.

Inflation risk

When inflation surpasses a predetermined level, the purchasing power of a particular quantity of money reduces. As a result of the fall in spending and consumption, overall market returns are reduced, resulting in a decline in investment.

Exchange Rate Risk

As the value of a currency reduces in comparison to other currencies, the value of the currency’s returns reduces as well. In such circumstances, all companies that conduct transactions in that currency lose money, and as a result, investors lose money as well.

Geopolitical Risks

When a country has significant geopolitical issues, the country’s companies are impacted. This can be mitigated by investing in multiple countries; but, if a country prohibits foreign investment and the domestic economy is threatened, the entire market of investable securities suffers losses.

Natural disasters

All companies in countries such as Japan that are prone to earthquakes and volcanic eruptions are at risk of such catastrophic calamities.

Following the Capital Asset Pricing Model (CAPM), the return on asset i, denoted by R_i can be decomposed as

img_SimTrade_return_decomposition

Where:

R_i the return of asset i
E(R_i) the risk premium of asset i
β_i the measure of the risk of asset i
R_M the return of the market
E(R_M) the risk premium of the market
R_M – E(R_M) the market factor
ε_i represent the specific part of the return of asset i

The beta of the asset with the market is computed as:

Beta

Where:

σ_i,m : the covariance of the asset return with the market return
σ_m² : the variance of market return

The total risk of the asset measured by the variance of asset returns can be computed as:

Decomposition of total risk

Where:

β_i² * σ_m² = systematic risk
σ_εi² = specific risk

In this decomposition of the total variance, the first component corresponds to the systematic risk and the second component to the specific risk.

Systematic risk analysis in recent times

The volatility chart depicts the evolution of implied volatility for the S&P 500 and US Treasury bonds – the VIX and MOVE indexes, respectively. Implied volatility is the price of future volatility in the option market. Historically, the two markets have been correlated during times of systemic risk, like as in 2008 (Figure 1).

Figure 1. Volatility trough time (VIX and MOVE index).

Sources: BlackRock Risk and Quantitative Analysis and BlackRock Investment Institute, with data from Bloomberg and Bank of America Merrill Lynch, October 2021 (BlackRock, 2021).

The VIX index has declined following a spike in September amid the equity market sell-off. It has begun to gradually revert to pre-Covid levels. The periodic, albeit brief, surges throughout the year underscore the underlying fear about what lies beyond the economic recovery and the possibility of a wide variety of outcomes. The MOVE index — a gauge of bond market volatility – has remained relatively stable in recent weeks, despite the rise in US Treasury yields to combat the important monetary policy to combat the effect of the pandemic. This could be a reflection of how central banks’ purchases of government bonds are assisting in containing interest rate volatility and so supporting risk assets (BlackRock, 2021).

The regime map depicts the market risk environment in two dimensions by plotting market risk sentiment and the strength of asset correlations (Figure 2).

Figure 2. Regime map for market risk environment.

Source: BlackRock Risk and Quantitative Analysis and BlackRock Investment Institute, October 2021 (BlackRock, 2021).

Positive risk sentiment means that riskier assets, such as equities, are outperforming less risky ones. Negative risk sentiment means that higher-risk assets underperform lower-risk assets.

Due to the risk of fast changes in short-term asset correlations, investors may find it challenging to guarantee their portfolios are correctly positioned for the near future. When asset correlation is higher (as indicated by the right side of the regime map), diversification becomes more difficult and risk increases. When asset prices are less correlated (on the left side of the map), investors have greater diversification choices.

When both series – risk sentiment and asset correlation – are steady on the map, projecting risk and return becomes easier. However, when market conditions are unpredictable, forecasting risk and return becomes substantially more difficult. The map indicates that we are still in a low-correlation environment with a high-risk sentiment, which means that investors are rewarded for taking a risk (BlackRock, 2021). In essence, investors should use diversification to reduce the specific risk of their holding coupled with macroeconomic fundamental analysis to capture the global dynamics of the market and better understand the sources of risk.

Why should I be interested in this post?

Market risks fluctuate throughout time, sometimes gradually, but also in some circumstances dramatically. These adjustments typically have a significant impact on the right positioning of a variety of different types of investment portfolios. Investors must walk a fine line between taking enough risks to achieve their objectives and having the proper instruments in place to manage sharp reversals in risk sentiment.

Useful resources

Academic research

Markowitz, H. 1952. Portfolio Selection. The Journal of Finance, 7(1): 77-91.

Mossin, J. 1966. Equilibrium in a Capital Asset Market. Econometrica, 34(4): 768-783.

Sharpe, W.F. 1963. A Simplified Model for Portfolio Analysis. Management Science, 9(2): 277-293.

Sharpe, W.F. 1964. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, 19(3): 425-442.

Business analysis

BlackRock, 2021. Market risk monitor

About the author

The article was written in April 2022 by Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022).

Systematic risk and specific risk

November 30, 2021 by Youssef LOURAOUI

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) presents the systematic risk and specific risk of financial assets, two fundamental concepts in asset pricing models and investment management theories more generally.

This article is structured as follows: we introduce the concept of systematic and specific risk. We then explain the mathematical foundation of this concept. We finish with an insight that sheds light on the relationship between diversification and risk reduction.

Portfolio Theory and Risk

The fraction of an individual asset’s total variance attributable to the variability of the total market portfolio is referred to as systematic risk, which is assessed by the asset’s covariance with the market portfolio. In the article systematic risk, we develop the economic sources of systematic risk: interest rate risk, inflation risk, exchange rate risk, geopolitical risk, and natural risk.

Additionally, due to the asset’s unique characteristics, an individual asset exhibits variance that is unrelated to the market portfolio (the asset’s non-market variance). Specific risk is the term for non-market variance, and it is often seen as minor because it can be eliminated in a large diversified portfolio. In the article specific risk, we develop the economic sources of specific risk: business risk and financial risk.

Mathematical foundations

Following the Capital Asset Pricing Model (CAPM), the return on asset i, denoted by R_i can be decomposed as

img_SimTrade_return_decomposition

Where:

R_i the return of asset i
E(R_i) the expected return of asset i
β_i the measure of the risk of asset i
R_M the return of the market
E(R_M) the expected return of the market
R_M – E(R_M) the market factor
ε_i the specific part of the return of asset i

The beta of the asset with the market is computed as:

Beta

Where:

σ_i,m : the covariance of the asset return with the market return
σ_m² : the variance of market return

Total risk can be deconstructed into two main blocks:

Total risk formula

The total risk of the asset measured by the variance of asset returns can be computed as:

Decomposition of total risk

Where:

β_i² * σ_m² = systematic risk
σ_εi² = specific risk

In this decomposition of the total variance, the first component corresponds to the systematic risk and the second component to the specific risk.

Effect of diversification on portfolio risk

Diversification’s objective is to reduce the portfolio’s standard deviation. This assumes an imperfect correlation between securities. Ideally, as investors add securities, the portfolio’s average covariance decreases. How many securities must be included to create a portfolio that is completely diversified? To determine the answer, investors must observe what happens as the portfolio’s sample size increases by adding securities with some positive correlation. Figure 1 illustrates the effect of diversification on portfolio risk, more precisely on total risk and its two components (systematic risk and specific risk).

Figure 1. Effect of diversification on portfolio risk

Source: Computations from the author.

The critical point is that by adding stocks that are not perfectly correlated with those already held, investors can reduce the portfolio’s overall standard deviation, which will eventually equal that of the market portfolio. At that point, investors eliminated all specific risk but retained market or systematic risk. There is no way to completely eliminate the volatility and uncertainty associated with macroeconomic factors that affect all risky assets. Additionally, investors can reduce systematic risk by diversifying globally rather than just within the United States, as some systematic risk factors in the United States market (for example, US monetary policy) are not perfectly correlated with systematic risk variables in other countries such as Germany and Japan. As a result, global diversification eventually reduces risk to a global systematic risk level.

You can download below two Excel files which illustrate the effect of diversification on portfolio risk.

The first Excel file deals with the case of independent assets with the same profile (risk and expected return).

Figure 2 depicts the risk reduction of total risk in as we increase the number of assets in the portfolio. We manage to reduce half of the overall portfolio volatility by adding five assets to the portfolio. However, the decrease becomes more and more marginal as we add more assets.

Figure 2. Risk reduction of the portfolio. img_SimTrade_systematic_specific_risk_1 Source: Computations from the author.

Figure 3 depicts the overall risk reduction of a portfolio. The benefit of diversification are more evident when we add the first 5 assets in the portfolio. As depicted in Figure 2, the diversification starts to fade at a certain point as we keep adding more assets in the portfolio. It can be seen in this figure how the specific risk is considerably reduced as we add more assets because of the effect of diversification. Systematic risk (market risk) is more constant and doesn’t change drastically as we diversify the portfolio. Overall, we can clearly see that diversification helps decrease the total risk of a portfolio considerably.

Figure 3. Risk decomposition of the portfolio. img_SimTrade_systematic_specific_risk_2 Source: Computations from the author.

The second Excel file deals with the case of dependent assets with the different characteristics (expected return, volatility, and market beta).

Academic research

A series of studies examined the average standard deviation for a variety of portfolios of randomly chosen stocks with varying sample sizes. Evans and Archer (1968) and Tole (1982) calculated the standard deviation for portfolios up to a maximum of twenty stocks. The results indicated that the majority of the benefits of diversification were obtained relatively quickly, with approximately 90% of the maximum benefit of diversification being obtained from portfolios of 12 to 18 stocks. Figure 1 illustrates this effect graphically.

This finding has been modified in two subsequent studies. Statman (1987) examined the trade-off between diversification benefits and the additional transaction costs associated with portfolio expansion. He concluded that a portfolio that is sufficiently diversified should contain at least 30–40 stocks. Campbell, Lettau, Malkiel, and Xu (2001) demonstrated that as the idiosyncratic component of an individual stock’s total risk (specific risk) has increased in recent years, it now requires a portfolio to contain more stocks to achieve the same level of diversification. For example, they demonstrated that the level of diversification possible in the 1960s with only 20 stocks would require approximately 50 stocks by the late 1990s (Reilly and Brown, 2012).

Figure 4. Effect of diversification on portfolio risk Source: Computation from the author.

You can download below the Excel file which illustrates the effect of diversification on portfolio risk with real assets (Apple, Microsoft, Amazon, etc.). The effect of diversification on the total risk of the portfolio is already significant with the addition of few stocks.

We can appreciate the decomposition of total risk in the below figure with real asset. We can appreciate how asset with low beta had the lowest systematic out of the sample analyzed (i.e. Pfizer). For the whole sample, specific risk is a major concern which makes the major component of risk of each stock. This can be mitigated by holding a well-diversified portfolio that can mitigate this component of risk. Figure 5 depicts the decomposition of total risk for assets (Apple, Microsoft, Amazon, Goldman Sachs and Pfizer).

Figure 5. Decomposition of total risk Source: Computation from the author.

You can download below the Excel file which deconstructs the risk of assets (Apple, Microsoft, Amazon, Goldman Sachs, and Pfizer).

Why should I be interested in this post?

If you’re an investor, understanding the source of risk is essential in order to build balanced portfolios that can withstand market corrections and downturns.

If you are a business school or university undergraduate or graduate student, this content will help you in broadening your knowledge of finance.

Useful resources

Academic research

Campbell, J.Y., Lettau, M., Malkiel, B.G. and Xu, Y. 2001. Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk. The Journal of Finance, 56: 1-43.

Evans, J.L., Archer, S.H. 1968. Diversification and the Reduction of Dispersion: An Empirical Analysis. The Journal of Finance, 23(5): 761–767.

Markowitz, H. 1952. Portfolio Selection. The Journal of Finance, 7(1): 77-91.

Mossin, J. 1966. Equilibrium in a Capital Asset Market. Econometrica, 34(4): 768-783.

Reilly, R.K., Brown C.K. 2012. Investment Analysis & Portfolio Management, Tenth Edition. 239-245.

Sharpe, W.F. 1963. A Simplified Model for Portfolio Analysis. Management Science, 9(2): 277-293.

Sharpe, W.F. 1964. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, 19(3): 425-442.

Statman, M. 1987. How Many Stocks Make a Diversified Portfolio?. The Journal of Financial and Quantitative Analysis, 22(3), 353–363.

Tole T.M. 1982. You can’t diversify without diversifying. The Journal of Portfolio Management. Jan 1982, 8 (2) 5-11.

About the author

The article was written in November 2021 by Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022).

Beta

November 20, 2021 by Youssef LOURAOUI

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) explains the concept of beta, one of the most fundamental concepts in the financial industry, which is heavily used in asset management to assess the risk of assets and portfolios.

This article is structured as follows: we introduce the concept of beta in asset management. Next, we present the mathematical foundations of the concept. We finish with an interpretation of beta values for risk analysis.

Introduction

The (market) beta represents the sensitivity of an individual asset or a portfolio to the fluctuations of the market. This risk measure helps investors to predict the movements of their assets according to the movements of the market overall. It measures the asset risk in comparison with the systematic risk inherent to the market.

In practice, the beta for a portfolio (fund) in respect to the market M represented by a predefined index (the S&P 500 index for example) indicates the fund’s sensitivity to the index. Essentially, the fund’s beta to the index attempts to capture the amount of money made (or lost) when the index increases (or decreases) by a specified amount.

Graphically, the beta represents the slope of the straight line through a regression of data points between the asset return in comparison to the market return for different time periods. It is a traditional risk measure used in the asset management industry. To give a more insightful explanation, a regression analysis has been performed using data for the Apple stock (APPL) and the S&P500 index to see how the stock behaves in relation to the market fluctuations (monthly data for the period July 2018 – June 2020). Figure 1 depicts the regression between Apple stock and the S&P500 index (excess) returns. The estimated beta is between zero and one (beta = 0.3508), which indicates that the stock price fluctuates less than the market index.

Figure 1. Linear regression of the Apple stock return on the S&P500 index return.

Source: Computation by the author (data source: Thomson Reuters).

Mathematical derivation of Beta

Use of beta

William Sharpe, John Lintner, and Jan Mossin separately developed key capital markets theory as a result of Markowitz’s previous works: the Capital Asset Pricing Model (CAPM). The CAPM was a huge evolutionary step forward in capital market equilibrium theory since it enabled investors to appropriately value assets in terms of systematic risk, defined as the market risk which cannot be neutralized by the effect of diversification.

The CAPM expresses the expected return of an asset a function of the risk-free rate, the beta of the asset, and the expected return of the market. The main result of the CAPM is a simple mathematical formula that links the expected return of an asset to these different components. For an asset i, it is given by:

CAPM risk beta relation

Where:

E(r_i) represents the expected return of asset i
r_f the risk-free rate
β_i the measure of the risk of asset i
E(r_m) the expected return of the market
E(r_m)- r_f the market risk premium.

The risk premium for asset i is equal to β_i(E(r_m)- r_f), that is the beta of asset i, β_i, multiplied by the risk premium for the market, E(r_m)- r_f.

In this model, the beta (β) parameter is a key parameter and is defined as:

CAPM beta formula

Where:

Cov(r_i, r_m) represents the covariance of the return of asset i with the return of the market
σ²(r_m) the variance of the return of the market.

Excel file to compute the beta

You can download below an Excel file with data for Apple stock returns and the S&P500 index returns (used as a representation of the market). This Excel file computes the beta of apple with the S&P500 index.

Interpretation of the beta

Beta helps investors to explain how the asset moves compared to the market. More specifically, we can consider the following cases for beta values:

β = 1 indicates a fluctuation between the asset and its benchmark, thus the asset tends to move at a similar rate than the market fluctuations. A passive ETF replicating an index will present a beta close to 1 with its associated index.
0 < β < 1 indicates that the asset moves at a slower rate than market fluctuations. Defensive stocks, stocks that deliver consistent returns without regarding the market state like P&G or Coca Cola in the US, tend to have a beta with the market lower than 1.
β > 1 indicates a more aggressive effect of amplification between the asset price movements with the market movements. Call options tend to have higher betas than their underlying asset.
β = 0 indicates that the asset or portfolio is uncorrelated to the market. Govies, or sovereign debt bonds, tend to have a beta-neutral exposure to the market.
β < 0 indicates an inverse effect of market fluctuation impact in the asset volatility. In this sense, the asset would behave inversely in terms of volatility compared to the market movements. Put options and Gold typically tend to have negative betas.

Why should I be interested in this post?

If you are a business school or university student, this post will help you to understand the fundamentals of investment.

Useful resources

Academic research

Fama, Eugene F. 1965. The Behavior of Stock Market Prices.Journal of Business 37: January 1965, 34-105.

Fama, Eugene F. 1967. Risk, Return, and General Equilibrium in a Stable Paretian Market. Chicago, IL: University of Chicago.Unpublished manuscript.

Fama, Eugene F. 1968. Risk, Return, and Equilibrium: Some Clarifying Comments. Journal of Finance, (23), 29-40.

Lintner, J. 1965a. The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. The Review of Economics and Statistics 47(1): 13-37.

Lintner, J. 1965b. Security Prices, Risk and Maximal Gains from Diversification. The Journal of Finance 20(4): 587-615.

Mangram, M.E., 2013. A simplified perspective of the Markowitz Portfolio Theory. Global Journal of Business Research, 7(1): 59-70.

Markowitz, H., 1952. Portfolio Selection. The Journal of Finance, 7(1): 77-91.

Mossin, J. 1966. Equilibrium in a Capital Asset Market. Econometrica 34(4): 768-783.

Sharpe, W.F. 1963. A Simplified Model for Portfolio Analysis. Management Science 9(2): 277-293.

Sharpe, W.F. 1964. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance 19(3): 425-442.

Business analysis

JP Morgan Asset Management, 2021. Glossary of investment terms: Beta

Man Institute, 2021. How to calculate the Beta of a portfolio to a factor

Nasdaq, 2021. Beta

About the author

The article was written in November 2021 by Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022).

Portfolio Theory and Risk

Sources of specific risk

Business risk

Financial risk

Mathematical foundations

Decomposition of returns

Why should I be interested in this post?

Related posts on the SimTrade blog

Useful resources

Academic research

About the author

Portfolio Theory and Risk

Interest rate risk

Inflation risk

Exchange Rate Risk

Geopolitical Risks

Natural disasters

Systematic risk analysis in recent times

Why should I be interested in this post?

Related posts on the SimTrade blog

Useful resources

Academic research

Business analysis

About the author

Portfolio Theory and Risk

Mathematical foundations

Effect of diversification on portfolio risk

Academic research

Why should I be interested in this post?

Related posts on the SimTrade blog

Useful resources

Academic research

About the author

Introduction

Mathematical derivation of Beta

Use of beta

Excel file to compute the beta

Interpretation of the beta

Why should I be interested in this post?

Related posts on the SimTrade blog

Useful resources

Academic research

Business analysis

About the author