Explain the risk–return relationship?

High risk means more return and vice verse under normal expectations..

I agree with the above intelligent and informative answers and i may add that mitigating risk is an important strategic action to be undertaken when entering any investment,the higher the risk the higher the return philosophy is only accepted by gamblers i believe.

We always aim for higher return with the lowest risk possible and it can be achieved in many ratios,i believe risk can be mitigated under certain conditions.

The principle that potential return rises with an increase in risk. Low levels of uncertainty (low-risk) are associated with low potential returns, whereas high levels of uncertainty (high-risk) are associated with high potential returns. According to the risk-return tradeoff, invested money can render higher profits only if it is subject to the possibility of being lost.

Because of the risk-return tradeoff, you must be aware of your personal risk tolerance when choosing investments for your portfolio. Taking on some risk is the price of achieving returns; therefore, if you want to make money, you can't cut out all risk. The goal instead is to find an appropriate balance - one that generates some profit, but still allows you to sleep at night.

agreed with gentlemen

if u will take more risk then u get more return and vice versa

A ratio used by many investors to compare the expected returns of an investment to the amount of risk undertaken to capture these returns. This ratio is calculated mathematically by dividing the amount he or she stands to lose if the price moves in the unexpected direction (i.e. the risk) by the amount of profit the trader expects to have made when the position is closed (i.e. the reward).

Simply more risk more return

I agree with the answers committed...

Entering a Business itself means taking a risk irrespective before entering a business you do S W O T Analysis still there is an element of risk involved.Higher the risk involved better are the chances of return and could be negative also.

simply risk means the uncertainty  of expected outcome or return of the investment.

The relation between risk and return is usually positive. the higher the risk or uncertainty the higher the return and lower risk  ensure lower return(almost certain)

Higher risk must be compensated by higher return.

The relationship between risk and return is often represented by a trade-off. In general, the more risk you take on, the greater your possible return.

This graphically represent the relationship it will be positive relation which mean more risk more returns and vice versa,

There are two main types of Risk:-

1- Systematic Risk influences a large number of assets. A significant political event.

2- Unsystematic Risk is sometimes referred to as "specific risk". This kind of risk affects a very small number of assets. An example is news that affects a specific stock

Other types of Risk  

1- Credit or Default Risk is the risk that a company or individual will be unable to pay the contractual interest or principal on its debt obligations.

2- Country Risk, refers to the risk that a country won't be able to honor its financial commitments. When a country defaults on its obligations.

3- Foreign Exchange Risk When investing in foreign countries you must consider the fact that currency exchange rates can change the price of the asset. 

4- Interest Rate Risk, is the risk that an investment's value will change as a result of a change in interest rates.

5- Political Risk is represents the financial risk that a country's government will suddenly change its policies. This is a major reason why developing countries lack foreign investment.

6- Market Risk, this is the most familiar of all risks. Also referred to as volatility, market risk is the the day-to-day fluctuations in a stock's price.