Is it true that the higher the returns p.a, the greater the risk?

The image above shows the efficient frontier.

According to the risk-return tradeoff, invested money can give higher profits only if the investor is willing to accept a higher possibility of losses. Risk is here often associated with the fluctuation of the price, hence standard deviation is used.​​​

Yes, that is the general rule! One such model is the the Capital Asset Pricing Model (CAPM) which is the one-factor model for investment returns.

CAPM describes the relationship between systematic risk and expected return for assets, particularly stocks.

The "beta" here referes to the sensitivity of a stock to market volatility. CAPM posits that the riskier the stock, the greater its expected return.

The safe investment rate of 3% here is based on a typical long term governemt bond. If you wish to get higher returns, naturally it would have to involve greater risks.

These risks can definitiely be reduced to an extent with throughout research and understanding of the market, along with steps taking to diversify your portfolio.​​​