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Bonds are fixed income securities. Therefore, their “value” depends mainly on interest rates. So factors that affect interest rates (risks) will have the greatest input on the value of a bond.
Equities cashflows are variable by nature; whether FCFF or FCFE. Therefore, equity value is affected by not only interest rates but also by cashflows.
Investors usually buy bonds in anticipation of a decrease in interest rates, so that they gain when interest rates decrease, and vice versa.