Risk Premiums on Risky Assets

嗨，从没放弃的小努力你好：

The covariance term is the discount for risk. Note that with a one-period defaultfree bond, the covariance term is zero because the future price is a known constant ($1) and the covariance of a random quantity with a constant is zero; and, intuitively, its value is given by the first term. Consequently, Equation 6 reduces to Equation 3 for the one-period default-free bond. But with the two-period default-free bond, the future price of $1 two periods in the future is known with certainty, but the price one period in the future is not. Consequently, the covariance term is not zero.
In general with risk-averse investors, the covariance term for most risky assets is
expected to be negative. That is, when the expected future price of the investment is
high, the marginal utility of future consumption relative to that of current consumption
is low. Alternatively, during bad economic times, investors expect a smaller labor
income in the future, so the marginal utility of future consumption, and hence the
inter-temporal rate of substitution, is higher. This relationship leads investors to
demand a higher required rate of trade-off of future for current consumption—as in
bad economic times when the labor market contracts. Bad economic times also tend
to be associated with declining risky asset pay-outs (declining earnings and dividends
for ordinary shares and defaults for bonds) leading to declining asset prices. The result
is that the covariance term for risky assets is typically negative, so the price of the
asset is lower. This negative covariance term results in a positive risk premium, ρt s i, ,
in Equation 1 because a lower price today leads to a higher return over time. Holding
all else constant, the risk premium term and the required return for an asset should
be higher, and its current market price is lower the larger the magnitude of the negative
covariance term.

同学你好，这是原版书的一个摘要，这里我们指的是无风险利率是one period default free government bonds，cov会收到有市场情绪、投资者情绪、甚至是期限等。这部分老师上课有强调，只要记结论即可，因为很多内容和我们之前讲的有些不连贯性。希望可以帮到你

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虽然现在很辛苦，但努力过的感觉真的很好，加油！