Question1.8 You are in a world where there are two assets: gold and stocks. Your estimate of the correlation between gold and stocks is negative -0.33. Based on these investment fundamentals, you have constructed a portfolio which is 25% invested in gold and 75% invested in stocks. You now learn that GPEC (a cartel of gold-producing countries) is going to vary the amount of gold produced depending on the price of stocks. It is going to produce more gold when the stock market is up, and it is going to produce less gold when the stock market is down. What effect will this have on the correlation between the two assets and on the weighting in your portfolio given to gold? The correlation increases, and the weight on gold increases. The correlation increases, and the weight on gold decreases. The correlation decreases, and the weight on gold decreases. The correlation is unchanged, and the weight on gold is unchanged. The correlation decreases, and the weight on gold increases. ResetMaximum marks: 2.5 Flag question undefined单项选择题
A
The correlation increases, and the weight on gold increases.
B
The correlation increases, and the weight on gold decreases.
C
The correlation decreases, and the weight on gold decreases.
D
The correlation is unchanged, and the weight on gold is unchanged.
E
The correlation decreases, and the weight on gold increases.

Question

Question1.8 You are in a world where there are two assets: gold and stocks. Your estimate of the correlation between gold and stocks is negative -0.33. Based on these investment fundamentals, you have constructed a portfolio which is 25% invested in gold and 75% invested in stocks. You now learn that GPEC (a cartel of gold-producing countries) is going to vary the amount of gold produced depending on the price of stocks. It is going to produce more gold when the stock market is up, and it is going to produce less gold when the stock market is down. What effect will this have on the correlation between the two assets and on the weighting in your portfolio given to gold? The correlation increases, and the weight on gold increases. The correlation increases, and the weight on gold decreases. The correlation decreases, and the weight on gold decreases. The correlation is unchanged, and the weight on gold is unchanged. The correlation decreases, and the weight on gold increases. ResetMaximum marks: 2.5 Flag question undefined单项选择题

A

The correlation increases, and the weight on gold increases.

B

The correlation increases, and the weight on gold decreases.

C

The correlation decreases, and the weight on gold decreases.

D

The correlation is unchanged, and the weight on gold is unchanged.

E

The correlation decreases, and the weight on gold increases.

BlackTom AI · Accepted Answer

Linking gold production to the stock market creates a new common driver between the two assets, so the correlation between gold and stocks increases (i.e., moves from its initial negative value toward zero or positive). Because the cartel will produce more gold when stocks are up and less when stocks are down, gold returns become more tied to stock movements and thus are less effective as a diversifier.

Relevant knowledge points and concepts
- Correlation and covariance: Cov(g,s) = ρ(gs) · σg · σs. If ρ increases, Cov increases (for given volatilities).
- Portfolio variance: Var(P) = w_g^2 σg^2 + w_s^2 σs^2 + 2 w_g w_s Cov(g,s). Higher covariance raises portfolio variance for given weights.
- Diversification and optimal weights: When an asset’s correlation with the rest of the portfolio increases (diversification benefit falls), the mean–variance optimal allocation to that asset typically falls.

Step-by-step reasoning and intermediate steps
1. The cartel’s rule ties gold supply decisions to stock prices, introducing a direct link; mathematically this raises ρ(gs) from −0.33 toward 0 or positive. Using Cov = ρ · σg · σs, Cov increases as ρ increases.
2. For fixed portfolio weights w_g and w_s, ∂Var(P)/∂Cov = 2 w_g w_s > 0, so increasing Cov (via higher ρ) increases portfolio variance.
3. To restore the portfolio to an optimal (lower-variance) position or to maximize risk-adjusted return given the reduced diversification, you reduce exposure to the asset that no longer provides as much negative covariance—here, gold. Thus the optimal weight on gold falls.

Why the correct answer is correct
- The cartel’s policy creates procyclical linkage between gold and stocks, increasing their correlation. Increased correlation reduces gold’s diversification benefit and raises the portfolio variance for a given gold weight; therefore an investor following mean–variance logic would decrease the weight on gold.

Why other options are incorrect (brief)
- “Correlation increases and weight on gold increases”: wrong because higher correlation reduces diversification, so allocation to the diversifier normally falls.
- Any option claiming the correlation decreases or is unchanged contradicts the fact that gold production is now tied to stock moves, which creates more comovement.
- “Correlation decreases and weight on gold increases” is the opposite of the expected effect.

Conclusion
The cartel’s behavior raises the correlation between gold and stocks and, as a consequence, the optimal portfolio weight on gold falls. This matches the provided answer: "The correlation increases, and the weight on gold decreases."