How To Calculate Expected Rates of Return?

Risk is the uncertainty that an investment will earn its expected rate of return. An investor who is evaluating a future investment alternative expects or anticipates a certain rate of return. 

As an example, an investor may know that about 30 percent of the time the rate of return on this particular investment was 10 percent. Using this information along with future expectations regarding the economy, one can derive an estimate of what might happen in the future.

The expected return from an investment is defined as:

The investor might estimate probabilities for each of these economic scenarios based on past experience and the current outlook as follows:

The computation of the expected rate of return [E(Ri)] is as follows:

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How To Compute Arithmetic Mean & Geometric Mean

Single Investment Given a set of annual rates of return (HPYs) for an individual investment, there are two summary measures of return performance. The first is the arithmetic mean return, the second is the geometric mean return. To find the arithmetic mean (AM), the sum (Σ) of annual HPYs is divided by the number of years (n) as follows:

Where:

ΣHPY = the sum of annual holding period yields

An alternative computation, the geometric mean (GM), is the nth root of the product of the HPRs for n years minus one.

Where:

π = the product of the annual holding period returns as follows:

To illustrate these alternatives, consider an investment with the following data:

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How To Measure Holding Period Yield & Annual Holding Period Yield

Holding Period Return (HPR) to an annual percentage rate is to derive a percentage return, referred to as the holding period yield (HPY). The HPY is equal to the HPR minus 1.

To derive an annual HPY, you compute an annual HPR and subtract 1. Annual HPR is found by:

Assume an investment that cost $250 and is worth $350 after being held for two years:

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What Is Historical Rates of Return?

When we invest, we defer current consumption in order to add to our wealth so that we can consume more in the future. Therefore, when we talk about a return on an investment, we are concerned with the change in wealth resulting from this investment. This change in wealth can be either due to cash inflows, such as interest or dividends, or caused by a change in the price of the asset (positive or negative).

When you are evaluating alternative investments for inclusion in your portfolio, you will often be comparing investments with widely different prices or lives. As an example, you might want to compare a $15 stock that pays no dividends to a stock selling for $250 that pays dividends of $10 a year. To properly evaluate these two investments, you must accurately compare their historical rates of returns. A proper measurement of the rates of return is the purpose of this section.

If you commit $200 to an investment at the beginning of the year and you get back $220 at the end of the year, what is your return for the period? The period during which you own an investment is called its holding period, and the return for that period is the holding period return (HPR). In this example, the HPR is 1.10, calculated as follows:

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Definition Of Investment

Investment can be defined as the current commitment of dollars for a period of time in order to derive future payments that will compensate the investor for (i) the time the funds are committed, (ii) the expected rate of inflation during this time period, and (iii) the uncertainty of the future payments. The “investor” can be an individual, a government, a pension fund, or a corporation. Similarly, this definition includes all types of investments, including investments by corporations in plant and equipment and investments by individuals in stocks, bonds, commodities, or real estate. This text emphasizes investments by individual investors. In all cases, the investor is trading a known dollar amount today for some expected future stream of payments that will be greater than the current dollar amount today.

Hence, the question is why people invest and what they want from their investments. They invest to earn a return from savings due to their deferred consumption. They want a rate of return that compensates them for the time period of the investment, the expected rate of inflation, and the uncertainty of the future cash flows. This return, the investor’s required rate of return, is discussed throughout this book. A central question of this book is how investors select investments that will give them their required rates of return.

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Welcome To Finance School With Md Edrich Molla

Finance School With Md Edrich Molla, is one of the pioneer online site since many years. Hope you'll get lot of benefits from here. 

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Efficient Market Hypothesis (EMH) Meaning

An efficient capital market is one in which security prices adjust rapidly to the arrival of new information, and, therefore, the current prices of securities reflect all information about the security.

Fama divided the overall efficient market hypothesis (EMH) and the empirical tests of the hypothesis into three sub-hypotheses depending on the information set involved: (1) Weak-form EMH, (2) Semistrong-form EMH, and (3) Strong-form EMH.

 

# TYPES OF EMH

Weak-form of EMH

The weak-form EMH assumes that current stock prices fully reflect all security market information, including the historical sequence of prices, rates of return, trading volume data, and other market-generated information, such as odd-lot transactions and transactions by market makers. Because it assumes that current market prices already reflect all past returns and any other security market information, this hypothesis implies that past rates of return and other historical market data should have no relationship with future rates of return (that is, rates of return should be independent). Therefore, this hypothesis contends that you should gain little from using any trading rule which indicates that you should buy or sell a security based on past rates of return or any other past security market data.

 

Semistrong-form EMH

The semistrong-form EMH asserts that security prices adjust rapidly to the release of all public information; that is, current security prices fully reflect all public information. The semistrong hypothesis encompasses the weak-form hypothesis, because all the market information considered by the weak-form hypothesis, such as stock prices, rates of return, and trading volume, is public. Notably, public information also includes all nonmarket information, such as earnings and dividend announcements, price-to-earnings (P/E) ratios, dividend-yield (D/P) ratios, price-book value (P/BV) ratios, stock splits, news about the economy, and political news. This hypothesis implies that investors who base their decisions on any important new information after it is public should not derive above-average risk-adjusted profits from their transactions, considering the cost of trading because the security price should immediately reflect all such new public information.

 

Strong-form EMH

The strong-form EMH contends that stock prices fully reflect all information from public and private sources. This means that no group of investors has monopolistic access to information relevant to the formation of prices. Therefore, this hypothesis contends that no group of investors should be able to consistently derive above-average risk-adjusted rates of return. The strong-form EMH encompasses both the weak-form and the semistrong-form EMH. Further, the strong-form EMH extends the assumption of efficient markets, in which prices adjust rapidly to the release of new public information, to assume perfect markets, in which all information is cost-free and available to everyone at the same time.

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What Is Beta?

Beta (β) is a Greek alphabet used in finance to denote the volatility or systematic risk of a security or portfolio compared to the market.

# HOW BETA WORKS

A beta coefficient shows the volatility of an individual stock compared to the systematic risk of the entire market. Beta represents the slope of the line through a regression of data points. In finance, each point represents an individual stock's returns against the market.

Beta effectively describes the activity of a security's returns as it responds to swings in the market. It is used in the capital asset pricing model (CAPM), which describes the relationship between systematic risk and expected return for assets. CAPM is used to price risky securities and to estimate the expected returns of assets, considering the risk of those assets and the cost of capital.

# HOW TO CALCULATE BETA?

A security's beta is calculated by dividing the product of the covariance of the security's returns and the market's returns by the variance of the market's returns over a specified period. The calculation helps investors understand whether a stock moves in the same direction as the rest of the market. It also provides insights into how volatile–or how risky–a stock is relative to the rest of the market.

# WHAT ARE THE BETA VALUES?

Beta Equal to 1; A stock with a beta of 1.0 means its price activity correlates with the market. Adding a stock to a portfolio with a beta of 1.0 doesn’t add any risk to the portfolio, but doesn’t increase the likelihood that the portfolio will provide an excess return.

Beta Less than 1; A beta value less than 1.0 means the security is less volatile than the market. Including this stock in a portfolio makes it less risky than the same portfolio without the stock. Utility stocks often have low betas because they move more slowly than market averages.

Beta Greater than 1; A beta greater than 1.0 indicates that the security's price is theoretically more volatile than the market. If a stock's beta is 1.2, it is assumed to be 20% more volatile than the market. Technology stocks tend to have higher betas than the market benchmark. Adding the stock to a portfolio will increase the portfolio’s risk, but may also increase its return.

Negative Beta; A beta of -1.0 means that the stock is inversely correlated to the market benchmark on a 1:1 basis. Put options and inverse ETFs are designed to have negative betas. There are also a few industry groups, like gold miners, where a negative beta is common.

Investors commonly evaluate two categories of risk. Systematic risk is the risk of the entire market declining, called un-diversifiable. Unsystematic, or diversifiable risk, is the uncertainty associated with an individual stock or industry. It is risk related to a company or sector and can be mitigated through diversification.

# IS BETA A GOOD MEASURE OF RISK?

Beta can provide some risk information, but it is not an effective measure of risk. Beta only looks at a stock's past performance relative to the S&P 500 and does not predict future moves. It also does not consider the fundamentals of a company or its earnings and growth potential.

# HOW DO INVESTORS INTERPRET A STOCK'S BETA?

A Beta of 1.0 for a stock means it has been as volatile as the broader market. If the index moves up or down 1%, so too would the stock, on average. Betas larger than 1.0 indicate greater volatility - so if the beta were 1.5 and the index moved up or down 1%, the stock would have moved 1.5%, on average. Betas less than 1.0 indicate less volatility: if the stock had a beta of 0.5, it would have risen or fallen just half a percent as the index moved 1%.

# IS BETA A HELPFUL MEASURE FOR LONG TERM INVESTMENTS?

While beta can offer useful information when evaluating a stock, it does have some limitations. Beta can determine a security's short-term risk and analyze volatility. However, beta is calculated using historical data points and is less meaningful for investors looking to predict a stock's future movements for long-term investments. A stock's volatility can change significantly over time, depending on a company's growth stage and other factors. 

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Definition Of Alpha

Alpha (α) is popularly used in investing to explain an investment strategy’s ability to gain high level of profit. Alpha is therefore also generally known as excess return or the abnormal rate of return comparing to a benchmark, when adjusted for risk.

We also can say, alpha is the excess return on an investment that is not a result of a general movement of the security market. Hence, a zero alpha would indicate that the portfolio or fund is going perfectly with the benchmark index and that the manager has not added or lost any additional value in the market.

# APPLICATION OF ALPHA IN INVESTMENT

Alpha is used in finance as a measure of performance, indicating when a strategy, trader, or portfolio manager has managed to beat the market return or other benchmark over some period. Alpha, often considered the active return on an investment, gauges the performance of an investment against a market index or benchmark that is considered to represent the market’s movement as a whole.

The excess return of an investment relative to the return of a benchmark index is the investment’s alpha. Alpha may be positive or negative and is the result of active investing. Beta, on the other hand, can be earned through passive index investing.

Active portfolio managers seek to generate alpha in diversified portfolios, with diversification intended to eliminate unsystematic risk. Because alpha represents the performance of a portfolio relative to a benchmark, it is often considered to represent the value that a portfolio manager adds to or subtracts from a fund’s return.

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Definition Of Behavioral Finance

 Behavioral finance can be defined as the study of investors’ psychology that impacts while making investment decision in the securities markets. It focuses on different psychological biases such as overconfidence, loss aversion, confirmation, anchoring and so on which directly impact investors’ decision making process on a particular security’s buying or selling.

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Definition Of Economics

In earth resources are limited but wants and demands are unlimited. It causes a lot of problems for the people around the globe to fulfill their sky-limit desires. Economics, the concept comes to us to clarify how to manage unlimited wants and demand by the limited resources.

Therefore, economics precisely can be defined as the studies of managing limitless needs, wants and demands by the limited assets or resources. It explains what to produce, how to produce, for whom to produce.   

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What Is Portfolio?

There is a saying that “Don’t keep all the eggs in a basket”. Suppose you keep many eggs in a basket. If basket falls, all eggs of the basket may be damaged at a time. But if you keep some of them in the different basket, one may be fallen down, rest will remain safe.  

Similarly, for investment, whole of your funds if you invest in a single security, price of the security goes down or becomes more volatile your investment may be lost. This is why you should invest funds into different securities or assets to minimize the risk and maximize the profit. It means risks should be diversified. So portfolio is the management and investment the whole funds into different securities or assets to diversify the risks and gain optimum level of profit.

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Definition Of Finance

Finance can be defined as the processes of planning and implementing on; from where to collect the funds (sources), how to utilize the funds (disbursement or investment), how to generate income from there (cost & inflows) and how to overall manage the funds (assets management and control).

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