Question

You can invest in a safe asset, in a risky asset, or in both. The safe asset has a guaranteed return of 3 per cent a year. The risky asset has an expected return of 4 per cent but it could be as much as 8 per cent or as little as 0 per cent. You decide to have some of your wealth in each asset. Now the expected return on the risky asset rises to 5 per cent; it could be as high as 9 per cent or as low as 1 per cent. Given the increase in the expected return on the risky asset, do you invest more of your wealth in the risky asset?

Short answer

Yes, you may invest more in the risky asset due to its increased expected return.

Step-by-step solution

Understand Risk and Return

The safe asset offers a guaranteed return of 3%, which is predictable and stable. The risky asset's return is variable, with an expected return initially at 4%, and a possible range between 0% and 8%.

Analyze Changes in Expected Return

With the new investment scenario, the expected return on the risky asset has increased from 4% to 5%, with a revised possible range between 1% and 9%.

Compare Risk-Reward Trade-off

The increase in the expected return on the risky asset improves its attractiveness since the potential average benefit increased while risks remain within a similar range. However, the stability of 3% return from the safe asset remains unchanged.

Decision Making - Risk Tolerance

If you have a higher risk tolerance, the increase in the expected return on the risky asset could justify increasing your investment in it. The trade-off is accepting more return variability for higher potential gains.

Conclusion

Given the increased expected return on the risky asset, you may decide to allocate more wealth into the risky asset due to the improved potential reward, provided you are comfortable with the associated risk.

Key concepts

Risk and Return

In finance, risk and return are closely connected concepts. Generally, risk is the potential for an investment to experience volatility or loss, while return is the gain or profit achieved.
For instance, choosing between a safe or risky asset involves comparing these two factors. A safe asset provides a stable and predictable return. It is less likely to fluctuate in value, meaning less risk.
On the other hand, a risky asset has a return that can vary greatly. Though it offers a higher potential return, it also poses a higher chance of loss. As such, investors continuously evaluate whether the potential returns outweigh the risks involved with each investment choice.

Safe Asset

A safe asset offers certainty and minimal risk, making it a popular choice for risk-averse investors. These assets have predictable outcomes because the returns are guaranteed or highly likely.
The safe asset in our discussion provides a guaranteed return of 3% per year, reflecting its reliability. This can be attractive for investors seeking stability without the concern of losing their initial investment.
Such assets are typically considered lower in potential return than riskier options but compensate with security. Ideal examples include government bonds or savings accounts, where returns are fixed and market fluctuations have minimal impact.

Risky Asset

Risky assets are a type of investment with uncertain returns. Unlike safe assets, the payout from a risky investment can vary significantly, affecting its reliability.
In our scenario, the risky asset initially had an expected return of 4%, which could range from 0% to 8%. Its attractiveness increased when the expected return rose to 5%, with a new range of 1% to 9%.
Investing in risky assets involves a trade-off: you may gain higher returns, but you also accept the potential for greater loss. Common examples of risky assets include stocks and commodities, where market dynamics regularly influence value.

• High potential rewards
• Increased variability of returns
• Higher risk of loss

Expected Return

The expected return is the average return an investor anticipates receiving on an investment. It is calculated based on probable outcomes weighted by their respective probabilities.
For the risky asset, the change in expected return—from 4% to 5%—means an anticipated higher average benefit over time. Despite fluctuations, such expectations can guide investor decisions.
Investors use expected return to gauge whether an investment aligns with their financial goals and risk tolerance. It plays a crucial role in decision-making by providing a benchmark to compare different investment opportunities. Therefore, a higher expected return usually enhances an investment's appeal, motivating investors to accept associated risks in pursuit of greater gains.