Covariance as Risk Premium

[quiteawesome]

Hi can someone help to explain the following? Can’t quite understand from the text provided in the Schweser textbook:
The covariance between the expected future price and the inter-temporal rate of substitution is a risk premium. Why is that so can someone please help to explain in simple terms?
Thanks in advance!

 

[bfry]

Covariance= [Sum( X-Xavg)*(Y-Yavg)] / N-1
Therefore this is just the average value of the deviations of X and Y around their mean. Therefore the more something deviates around its mean values the more “risk” there is. A covariance close to +/- infinity would mean the average value of the deviations around the mean is really high - i.e. more risk. Thus you would command a larger premium.
In terms of the material - if the inter-temporal rate of substitution and expected future spot price deviate from their average values a lot this will cause the covariance to be closer to +/- infinity. Again you would command more premium for this asset.

 

[quiteawesome]

Thanks for the comments.
Can someone provide additional insight on why the covariance is negative?

 

[abeshak sindhi]

If the covariance between future payoff future consumption is postive this means that during bad times when my consumption increases the payoff from this asset also increases.the risk premium demanded will be low because it is a good hedge against badtimes. Negative means that during bad times the payoff from the asset is low therefore risk premium demanded is high hence negative covariance.