# Relationship between risk and return for efficient portfolio

The efficient portfolio consists of investments that provide the greatest return for . Calculating the Covariance and Coefficient of Correlation between 2 Assets. The variance of the rate of return of a portfolio consisting of The smaller the correlation between the assets the lower the portfolio variance. . the inputs required to construct an efficient portfolio. The relationship between the risk and required return is. normally . reduce risk, and to create an efficient portfolio, the assets. that are best.

The risk of a portfolio composed of these assets can be reduced to zero. If there is no discernible pattern to the up and down cycles of 1 investment compared to another, then the 2 investments have no covariance. An uncorrelated investment pair would have a correlation coefficient close to zero.

Note that since the correlation coefficient is a statistical measure, a perfectly uncorrelated pair of investments will rarely, if ever, have an exact correlation coefficient of zero.

The most diversified portfolio consists of securities with the greatest negative correlation. A diversified portfolio can also be achieved by investing in uncorrelated assets, but there will be times when the investments will be both up or down, and thus, a portfolio of uncorrelated assets will have a greater degree of risk, but it is still significantly less than positively correlated investments.

### Portfolio Returns and Risks; Covariance and the Coefficient of Correlation

However, even positively correlated investments will be less risky than single assets or investments that are perfectly positively correlated.

However, there is no reduction in risk by combining assets that are perfectly correlated. Correlations can change over time and in different economic conditions. For instance, during the late 's, stock prices increased significantly, then crashed in Interest rates were lowered to boost the economy, which caused real estate prices to increase significantly from - Hence, real estate prices were increasing while stocks were either declining, or not increasing by nearly the same rate.

## Risk and return

This reflects the general negative correlation between the stock market and the real estate market. The real estate market was forming a bubble due to the extremely low interest rates at the time. The bubble finally burst inand especiallyleading to the — credit crisis. The fast increase in prices was not due to demand, but due to the transfer of money from assets doing poorly—stocks and real estate—to commodities and future contracts.

## Portfolios Returns and Risks

In other words, it was another bubble. However, as credit dried up, due to the prevalence of many defaults of subprime mortgages, almost every investment came crashing down in September and October of Only United States Treasurieswhich are virtually free of credit-default risk, rose significantly in price, driving their yields down proportionately, with the yields of short-term T-bills reaching almost zero.

A major concern of investors is that their investment portfolios will not generate returns sufficient to meet their goals. This possibility is referred to as "shortfall risk", and deserves serious consideration. For long-term returns, it is more appropriate to estimate the dispersion of accumulated wealth also referred to as terminal wealth dispersion rather than the deviation of returns over relatively short time periods, such as annually.

Annualized T-Bill Yield and Inflation Rate - [9] Money market securities are often referred to as risk-free assets, especially the shorter-maturity securities such as day T-Bills. This is because the short-term return is known with relative certainty at the time the investment is made. There is absolute certainty in the nominal return of a T-Bill assuming the U.

### Risk and return - Bogleheads

If longer time periods are considered, even money market securities have some risk. This is because the effect of unexpected inflation on returns is uncertain over longer time periods.

Although money market security rates usually respond relatively quickly to changes in inflation, this is not always the case. Figure 2 illustrates the longer-term uncertainty of real returns on day T-Bills. Of course in return for this reduction in uncertainty, investors must accept lower expected returns. Marketable inflation-indexed securities also have other risks, such as interest rate risk i.

- Concept of Risk-Return in Portfolio Context (With Formulas)

During this same time period other U. For example, to meet a nominal liability at a specified future date, a zero-coupon US government bond maturing on that date is essentially risk free.

Nevertheless, short-term T-bills usually are considered to be risk-free assets in portfolio theory, and in practice investors treat a broader range of money market securities as risk free.

If the investor is not simply gambling, there must be some financial incentive, such as the expectation of a higher rate of return. This logic leads to the conclusion that an investment in a risky asset depends on the investor's expectation of a higher rate of return as well as his or her level of risk aversion. Note that a higher expected return does not guarantee a higher realized return.

Because by definition returns on risky assets are uncertain, an investment may not earn its expected return. The amount by which a risky asset is expected to provide a higher rate of return than the risk-free rate is the asset's risk premium the risk-free rate is the rate of return on a risk-free asset, such as a T-bill.

If the risk premium of stocks were zero, then a rational, risk-averse investor would have no incentive to invest in them.

On the other hand, a gambler might "invest" in something with a zero or even negative risk premium for entertainment value, or in the irrational expectation of hitting a jackpot.