Not only do stock and bond prices not move together, they most often move in opposite directions. This is because they are much different investments and usually attract very different buyers. Bonds are corporate borrowings, so their prices depend on the credit standing of the issuer and prevailing interest rates. Conversely, stocks are corporate ownership, with prices typically dependent upon strong or weak economies and company profit projections.
Bonds are offered by companies needing funds. Often, their cash needs are both short- and long-term. The attraction and pricing of bonds is influenced by the credit standing of the company and the interest rate offered. Institutional investors, such as universities, insurance companies and pension funds, favor bonds because of their security and interest payments. Some companies, particularly those with some credit problems, issue convertible bonds that can be swapped for corporate stock at designated dates in the future.
When you buy stock, you're becoming an owner in a company. Unlike bonds, which organizations use to borrow money, you are contributing capital to the corporation if you buy stock directly from the company, or acquire an ownership interest when you buy stock from a third party or the market. Stock prices move with the economy's strengths/weaknesses or the profit prospects of individual companies. There is no interest rate or promise of repayment. Stockholders have more risk but also the potential of greater profits.
Companies using bonds to raise money depend on their credit strength and stability of interest rates to sell their bonds. Corporations selling stock raise money, as capital, by offering shares that investors want. The dramatic difference, debt and ownership, in these two investments historically motivates pricing movements that go in opposite directions. The security of bonds, along with their promised return, interest, enjoy rising prices in periods of economic uncertainty. When the economy is "hot," stocks, along with their expectations of profit, become more attractive than bonds.
Volatility is the tendency of investments to increase or decrease. High volatility means that investment values rise or fall frequently. Low volatility means that market values move up or down less frequently. Bonds, because of corporate promises of repayment and interest payments, have less volatility than stocks, which can move dramatically in price daily, sometimes hourly. Bond investors like the corporate guarantees and stability bonds enjoy, except in rapidly moving interest rate environments. Stock investors bet they'll enjoy much higher returns, profits, along with accepting the higher risk of loss.