Do bonds reduce the overall risk of an investment portfolio?

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute .

x: 12 03 92 33 12 52 6 -12 -12 -23

y: 9 -3 26 15 24 17 15 -3 -4 -9