Suppose that the market price of risk for gold is zero. If...

Suppose that the market price of risk for gold is zero. If the storage costs are $1 \%$ per annum and the risk-free rate of interest is $6 \%$ per annum, what is the expected growth rate in the price of gold? Assume that gold provides no income.

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Key Concepts

Risk-Neutral Pricing

Risk-neutral pricing is a framework in financial economics where all assets are assumed to grow at the risk-free rate when adjusted for risk. Under this measure, expected asset returns are not influenced by their risk characteristics, and any risk premium is removed, simplifying the valuation of derivatives and other financial instruments.

Cost-of-Carry Model

The cost-of-carry model explains the relationship between the spot and forward prices of a commodity. It accounts for the various costs associated with holding the commodity, such as storage costs, financing costs, and any convenience yield. When income from the asset is absent, storage costs directly reduce the effective return obtained from holding the asset.

Expected Price Growth Derived from Arbitrage

In an arbitrage-free market, the expected growth rate of a commodity's price under risk-neutral conditions equals the risk-free rate minus any carrying costs, such as storage fees. This is because investors expect the net benefit of holding the asset (after incurring costs) to match the riskless return available in the market.

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