{"id":7690,"date":"2022-04-20T20:10:02","date_gmt":"2022-04-20T19:10:02","guid":{"rendered":"https:\/\/www.simtrade.fr\/blog_simtrade\/?p=7690"},"modified":"2022-04-20T20:10:02","modified_gmt":"2022-04-20T19:10:02","slug":"returns","status":"publish","type":"post","link":"https:\/\/www.simtrade.fr\/blog_simtrade\/returns\/","title":{"rendered":"Returns"},"content":{"rendered":"

\"Jayati<\/a><\/p>\n

In this article, Jayati WALIA<\/a> (ESSEC Business School, Grande Ecole<\/i> Program – Master in Management, 2019-2022) explains how returns of financial assets are computed and their interpretation in the world of finance.<\/p>\n

Introduction<\/h2>\n

The main focus of any investment in financial markets is to make maximum profits within a coherent risk level. Returns in finance is a metric that inherently refers to the change in the value of any investment. Positive values of returns are interpreted as gains whereas negative values are interpreted as losses.<\/p>\n

Returns are generally computed over standardized frequencies such as daily, monthly, yearly, etc. They can also be computed for specific time periods such as the holding period for ease of comparison and analysis.<\/p>\n

Computation of returns<\/h2>\n

Consider an asset for a time period [t -1, t] with an initial price Pt-1<\/sub> at time t-1 and final price Pt<\/sub> at time t (one period, two dates). Different forms of defining returns for the asset over period [t -1, t] are discussed below.<\/p>\n

Arithmetic (percentage) returns<\/h3>\n

This is the simplest way for computation of returns.<\/p>\n

The return over the period [t -1, t], denoted by R<\/i>t<\/sub>, is expressed as:<\/p>\n

\"Arithmetic<\/p>\n

Logarithmic returns<\/h3>\n

Logarithmic returns (or log returns) are also used commonly to express investment returns. The log return over the period [t-1, t], denoted by R<\/i>t<\/sub> is expressed as:<\/p>\n

\"Logarithmic<\/p>\n

Log returns provide the property of time-additivity to the returns which essentially means that the log returns over a given period can be simply added together to compute the total return over subperiods. This feature is particularly useful in statistical analysis and reduction of algorithmic complexity.<\/p>\n

\"Logarithmic<\/p>\n

Log returns are also known as continuously compounded returns because the rate of log returns is equivalent to the continuously compounding interest rate for the asset at price P0<\/sub> and time period t.<\/p>\n

\"img_SimTrade_compounded_returns\"<\/p>\n

Link between arithmetic and logarithmic returns<\/h3>\n

The arithmetic return (R<\/i>ari<\/sup>) and the logarithmic return (R<\/i>log<\/sup>) are linked by the following formula:<\/p>\n

\"Relation<\/p>\n

Components of total returns<\/h2>\n

The total return on an investment is essentially composed of two components: the yield and the capital gain (or loss). The yield refers to the periodic income or cash-flows that may be received on the investment. For example, for an investment in stocks, the yield corresponds to the revenues of dividends while for bonds, it corresponds to interest payments.<\/p>\n

On the other hand, capital gain (or loss) refers to the appreciation (or depreciation) in the price of the investment. Thus, the capital gain (or loss) for any asset is essentially the price change in the asset.<\/p>\n

Total returns for a stock over the period [t -1, t], denoted by Rt<\/sub>, can hence be expressed as:<\/p>\n

\"Total<\/p>\n

Where
\n   Pt<\/sub>: Stock price at time t
\n   Pt-1<\/sub>: Stock price at time t-1
\n   Dt-1,t<\/sub>: Dividend obtained over the period [t -1, t]<\/p>\n

Price changes and returns<\/h2>\n

Consider a stock with an initial price of 100\u20ac at time t=0. Suppose the stock price drops to 50\u20ac at time t=1. Thus, there is a change of -50% (minus sign representing the decrease in price) in the initial stock price.<\/p>\n

Now for the stock price to reach back to its initial price (100\u20ac in this case) at time t=2 from its price of 50\u20ac at time t=1, it will require an increase of (100\u20ac-50\u20ac)\/50\u20ac = 100%. With arithmetic returns, the increase (+100%) has to be higher than the decrease (-50%).<\/p>\n

Similarly, for a price drop of -25% in the initial stock price of 100\u20ac, we would require an increase of 33% in the next time period to reach back the initial stock price. Figure 1 illustrates this asymmetry between positive and negative arithmetic returns.<\/p>\n

Figure 1. Evolution of price change as a measure of arithmetic returns.
\n\"img_SimTrade_price_change_evolution\"
\nSource: computation by the author.<\/p>\n

If the return is defined as a logarithmic return, there is a symmetry between positive and negative logarithmic returns as illustrated in Figure 2.<\/p>\n

Figure 2. Evolution of price change as a measure of logarithmic returns.
\n\"img_SimTrade_price_change_evolution\"
\nSource: computation by the author.<\/p>\n

You can also download below the Excel file for computation of arithmetic returns and visualise the above price change evolution.<\/p>\n

\"Download<\/a><\/p>\n

Internal rate of return (IRR)<\/h2>\n

Internal rate of return (IRR) is the rate at which a project undertaken by the firm break\u2019s even. It is a financial metric used by financial analysts to compute the profitability from an investment and is calculated by equating the initial investment and the discounted value of the future cashflows i.e., making the net present value (NPV) equal to zero. The IRR is the sprecail value of the discount rate which makes the NPV equal to zero.<\/p>\n

The IRR for a project can be computed as follows:<\/p>\n

\"IRR<\/p>\n

Where,
\n   CFt<\/sub> : Cashflow for time period t<\/p>\n

The higher the IRR from a project, the more desirable it is to pursue with the project.<\/p>\n

Ex ante and ex post returns<\/h2>\n

Ex ante and ex post are Latin expressions. Ex ante refers to \u201cbefore an event\u201d while ex post refers to \u201cafter the event\u201d. In context of financial returns, the ex ante return corresponds to prediction or estimation of an asset\u2019s potential future return and can be based on a financial model like the Capital Asset Pricing Model (CAPM). On the other hand, the ex post return corresponds to the actual return generated by an asset historically, and hence are lagging or backward-looking in nature. Ex post returns can be used to forecast ex ante returns for the upcoming period and together, both are used to make sound investment decisions.<\/p>\n

Related posts on the SimTrade blog<\/h2>\n

   ▶ Jayati WALIA Standard deviation<\/a><\/p>\n

   ▶ Rapha\u00ebl ROERO DE CORTANZE The Internal Rate of Return<\/a><\/p>\n

   ▶ J\u00e9r\u00e9my PAULEN The IRR function in Excel<\/a><\/p>\n

   ▶ L\u00e9opoldine FOUQUES The IRR, XIRR and MIRR functions in Excel<\/a><\/p>\n

About the author<\/h2>\n

The article was written in April 2022 by Jayati WALIA<\/a> (ESSEC Business School, Grande Ecole<\/i> Program – Master in Management, 2019-2022).<\/p>\n","protected":false},"excerpt":{"rendered":"

In this article, Jayati WALIA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022) explains how returns of financial assets are computed and their interpretation in the world of finance. Introduction The main focus of any investment in financial markets is to make maximum profits within a coherent risk level. Returns in finance … Read more<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[5,10],"tags":[51,357,500],"class_list":["post-7690","post","type-post","status-publish","format-standard","hentry","category-contributors","category-financial-techniques","tag-arithmetic-return","tag-logarithmic-return","tag-return"],"yoast_head":"\nReturns - SimTrade blog<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.simtrade.fr\/blog_simtrade\/returns\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Returns\" \/>\n<meta property=\"og:description\" content=\"In this article, Jayati WALIA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022) explains how returns of financial assets are computed and their interpretation in the world of finance. 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