The steep decline in the bond market — and the accompanying move up in interest rates — will only stop if the sell-off in stocks accelerates, according to Barclays. Strategist Ajay Rajadhyaksha said in a note to clients late Wednesday that the rise in market interest rates, which move opposite to bond prices, won't end until investors start to dramatically cut their exposure to stocks. "Despite the breathtaking sell-off in longer rates, we do not see a clear catalyst to stem the bleeding. Data are unlikely to weaken quickly or enough to help bonds, which suggests that risk assets have to keep falling for longer rates eventually to find a bid," Rajadhyaksha said. The 10-year Treasury yield jumped above 4.8% earlier this week, hitting its highest mark in 16 years. The 30-year Treasury yield topped 4.9%, up from less than 4% as recently as July. US10Y 1M mountain The 10-year Treasury yield hit its highest level since 2007 this week. "There is no magic level of yields that, when reached, will automatically draw in enough buyers to spark a sustained bond rally," the strategist said. Equities have already been under pressure, with the S & P 500 down about 5% over the past month. But that broad market index is still positive for the year. If stocks fall further, "bonds will likely benefit from the portfolio effect" as investors shift out of equities into safer assets such as Treasurys, the strategist said. "Despite favorable seasonals, we believe that the eventual path to bonds' stabilizing lies through a further re-pricing lower of risk assets. Absent that, there is no sustained bond stabilization and, given how risk assets are finally responding to bonds, no stabilization in risk assets, either. We believe stocks have substantial room to re-price lower before bonds stabilize," Rajadhyaksha said. Outside of a decline in stocks, the other way for bonds to stabilize is if investors feel a recession is imminent, according to Barclays, which could in turn weigh on stocks. "Another way for bonds to catch a bid is for U.S. data to worsen — sharply and quickly," the note said. Traders often look to the Federal Reserve in times of bond market stress, as the central bank has in the past stepped in to calm the Treasury market. But the central bank is currently shrinking its balance sheet by selling bonds, and it is unlikely to reverse course given that inflation is still running far above the Fed's 2% target, Rajadhyaksha said. "The only way the Fed could help longer yields is by hiking so aggressively that markets are convinced a recession is imminent and rush to buy longer rates. But that is extremely unlikely as well. The Fed is likely simply to stay the course," the note said. — CNBC's Michael Bloom contributed reporting.