"What is the relationship between bond prices, interest rates, and other macroeconomic variables?"
The behaviour of bond prices can seem a little mysterious at the best of times. Let me try to demystify them a little in this post.
Let's start with the relationship between bond prices and interest rates. A bond is an instrument that guarantees to pay a fixed sum of money at some point in the future, perhaps with regular interest payments along the way. Once the bond is issued, the amount that the bond will pay and the interest are both fixed. However, the value of the bond can vary with market conditions.
Bond prices and interest rates move in inverse to each other. To see why, consider a bond that will pay out $1 at maturity (principle plus interest), with no additional interest payments along the way. If that bond has a price today of $P, the return (or interest rate) on that bond is given by r = (1-P)/P. Clearly an increase in P corresponds to a decrease in r, and vice versa.
That's the easy part. Now what about the relationship between bond prices and the macroeconomy? The simplest way to understand this is to think about the relationship between the return (or interest rate) on bonds, which tend to be relatively long term, and short term interest rates.
Consider an investor deciding whether to invest in long-term bonds or leave their wealth in a savings account. In the margin, they should be indifferent between the two. That means that the return on a bond must be related to the expected return from leaving your money in your savings account over the same period of time, adjusting for factors such as liquidity (savings accounts are more liquid- easier to spend- than bonds, and therefore offer lower returns on average). This idea lies begind the "expectations hypothesis" (see here
for a concise explanation). It allows us to reduce a long-term interest rate to a sequence of short-term interest rates.
So bond prices depend on expected future short-term interest rates. Then where do short-term interest rates come from? In the case of Hong Kong, our short-term interest rates depend heavily on US short term-interest rates, since any large deviation between the two would open up an arbitrage opportunity that investors could capitilise on (see here and here for more on this).
Then where do US short-term interest rates come from? The shortest term rate is the Federal Funds rate that is set by the Federal Reserve Board. It's the interest rates that major financial corporations pay/receive when receiving/making loans to meet their daily settlement needs. It also tends to be a trend-setting rate that influences other short-term interest rates, such as those you receive on a savings account.
Putting these pieces of the puzzle together, long-term interest rates depend on the expected future behaviour of the Federal Reserve. So what determines the interest rate setting behaviour of the Federal Reserve? To answer that, we'd need to look at what the Federal Reserve is trying to achieve when it adjusts interest rates.
The Federal Reserve has the job of trying to ensure that the US economy grows as fast as possible without triggering too much inflation (for a more precise definition, click here). If they think the economy is going to grow too fast, they'll raise short term interest rates. And if they think the economy is going to grow to slow, they'll lower interest rates.
Investors try to guess which way the Federal Reserve is leaning when deciding whether to buy bonds or not. If they think that the Federal Reserve is thinking that the economy is going to grow too fast, they expect future short term interest rates to rise. As a result, they're less willing to hold bonds, so the price of bonds falls today.
In the last few weeks, the price of bonds has been dropping dramatically, and as a result their interest rates have been rising. That's because investors believe that the likelihood of the Fed raising rates in the future is increasing.
Of course they might be wrong. In that case, bond prices can increase or decrease without really signalling anything about the future behaviour of the Federal Reserve, or for that matter, the macroeconomy more broadly.
So coming back to the original question, what macroeconomic variables influence bond prices? Anything that would help to indicate whether interest rates are likely to rise or drop in future. That includes anything that the Federal Reserve is likely to look at when trying to determine the future path of the economy. And that covers virtually all macroeconomic variables!