It is true that to achieve better return, one need to take risk. Generally, yes. However, conversely not necessrily true every time.

On direct risk-return relationship there are studies with mixed results. Just as there are different views on the measurement models (eg. CAPM, TFM, APT, etc.). Might be interesting to the question shared.

https://www.researchgate.net/post/What_do_you_think_of_the_health_of_the_Capital_Asset_Pricing_Model

this is an assumption that may or may not hold. First measuring risk using historical data is problematic...but no better way has been devised yet. Second even where the relationship holds, it could be just a self fulfilling prophecy, something that is taken for granted but that could be true (I will attach a paper below). Granted, stocks tend to exhibit higher returns than fixed incomes.....whether risk is the cause is another question.

please download and read- Economics language and assumptions: How theories can be self fulfilling. academy of management review.......this was one of best article winners.

Theoretically, the direct relationship between risk and return is strong and logical. However, to verify whether the direct relationship holds is an empirical question and it can only be answered empirically. Empirical evidence on risk-return relationship is mixed.

Risk and return, has traditionally been thought to be corelated – on a larger scale. Of course you have to take account for the law of large numbers, and thus accept that individual events or returns on investments can fall considerably short of the expected. But as B.T Matemilola writes it is the only logical correlation today.

The problem is it is not consistently observable in real life!

In 1980 Bowman did a large accounting survey of high risk companies, and he could not find that relationship:

http://dspace.mit.edu/bitstream/handle/1721.1/48928/riskreturnparado00bowm.pdf?sequence=1

Thus Bowman’s Paradox was defined. It was recently termed one of the most enduring economic paradoxes. It seems that the risk return relationship may hold for investments that are relative small compared to the investor.

Recent work has shown that when undertaking long term investments, the risk & return relationship fails. When you increase risk beyond a certain thresh hold the return drops. A new risk cost has been named the structural risk cost, to cover this observation. Its existance has been shown in an experiment.

So Bowmans paradox is not realy a paradox any more, as it is now fully expected that large risk (relatively) will reduce the return for an investor.

In the future we have to split such questions in "risk and return for small risk" and "Risk and Return for Large risk" where large risks are defined as risks that can result in financial challenges (shocks to the capital) that exceed the capital reserve of the investor.

Article Risk, resources and structures: Experimental evidence of a n...

Risk-Return trade-off is one of the axioms upon which finance and economics rest. It is also strengthened by the assumption of human rationality in finance. In spite of the commonsense in this axiom, it may be time and space variant, so that it is not always evident  as changes occur in space and time. That the axiom is not always true is quite good for the subject of finance because it provides the intrigue and excitements needed in financial scholarship and practice. Recall that much of the works for the award of Nobel Prize for Economics in 1990 was in the area of risk and its measurement. See one of the excitements in the following article:

http://www.ccsenet.org/journal/index.php/ijef/article/view/40722

Daibi W Dagogo,

Risk & Return, being an axiom, indicates that it has played an important role in refining  and creating investment and financing theory, and shaping the society. It does not in any way imply a state of perfection.

I completely agree with the Risk & Return litterature being pivotal for our financial and socio-economic theories.

However note, in theory, the Risk & Return litterature can be seriosuly flawed, as long as it, when presented,  represented an improvement compared to previous theory.

And in the light of recent research that has shown that it is flawed, it is not advisd to rely on the outcome of i.e. Real Option evaluations for large decisions, that can challenge the stability of the agent. For this type of investments, current theory will underestimate the risk cost, and lead to an overly positive assessment.

This is also the conclusion of the work done in the area of distress cost, though the problem is larger, and more fundamental, than what this narrow field of research concludes. 

I think there's a difference between what you get and what you ask for. 

Generally, you'll ask for higher expected return when risk is higher, because you may not get much in adverse scenarios.

hence, I am not sure