If the Risk Free Rate increases, then Cost of equity also increases as per CAPM model and therefore price of stock decreases as the value of stock inversely proportionate with the cost of equity.
Also, increased risk free rate will attract additional buyer from equity to risk free debt security which will result in massive selling in equity, thereby price of stock will decrease.
Also reverse scenario is also true, reduced risk free rate indicates the stability in the economy and people will invest more in the equity market rather than fixed income security.
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