Consider a risk averse investor whose preferences satisfy decreasing relative risk aversion. There are two types of assets: a risky asset and a safe asset. Assume that the investor invests a positive proportion of his total wealth in the risky asset. Does the proportion of his total wealth invested in the risky asset increase in his wealth? Explain your answer as precisely as possible.
To establish the fact that risk-averse investor will invest more in risky assets as wealth increases, we need a few assumptions:
1) return from safe asset is less than risky asset.
2) the risky asset has two types of returns with different probability, one positive return and a negative return.
Accordingly, the overall return from risky asset should be positive without which a risk-averse investor will not invest in a risky asset. Thus, we can establish that with increase in wealth, investor will increase investment in the risky asset.
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