# Fundamental reason for this issue

Although future and forward share the same underlying asset, their prices diverge because of their different features. The main reason that future price is different from forward price is the daily settlement, which means the future contract holder could trade their futures anytime before the maturity, while the forward contract is an OTC contract.

Then, after knowing their different features, let’s look at why this feature could change their prices. The key determinant is the correlation of underlying asset price and the interest rate. When they have a positive correlation, future price is higher. When negative correlation, forward price is higher. Let’s use an example to illustrate this idea: suppose you have a future on stocks and it has a positive correlation with the interest rate when the interest rate goes higher, the stock price would increase under our assumption. Due to market to market price, the future and forward price also increase. During this time, the long future holder could reinvest their extra cash at a higher rate, that’s an extra advantage. Similarly, when interest rate goes down, future and forward prices go down, long future holder still have a right to borrow extra money at a lower rate. Therefore, when having a positive correlation, the future price is always enjoying the interest benefit and it has a higher price than forward contract.

*source: https://www.youtube.com/watch?v=5tfdtZRqnSc*

# The correlation of underlying price and interest rate

Now, things come to the analysis of the correlation. Since I was confused by different professors at a different time when they claimed that future price is higher or lower than the forward price without talking about the correlation of underlying asset and interest rate, let me further explain this correlation under different conditions.

## Stocks

This article “How Interest Rates Affect The Stock Market” gives a comprehensive view of the mechanism of how int rate affects the stock price. Since the int rate affects almost EVERYTHING, the conclusion is vague. So, we may need to see this correlation empirically, and Sam Ro has an article about this issue (Rising interest rates usually come with higher stock prices).

I just refer his explanation here.

Interest rates have been on the rise in recent months. At 2.26% today, the 10-year US Treasury note yield is way up from its January 30 low of 1.63%.

But are rising interest rates bad for stocks? It might seem so. After all, higher rates mean higher borrowing costs for corporations.

However, history suggests otherwise.

“We note that since 1998, changes in bond yields and equity performance have been positively correlated, (i.e. equities and bond yields have risen together), as we can see below,” Credit Suisse’s Andrew Garthwaite said in a note to clients on Friday.

Credit Suisse

There are a few theories to justify this trend.

“[T]ypically a rise in inflation expectations is positive for equities (with equities being an inflation hedge) when inflation expectations rise from sub 2% to over 2%,” Garthwaite added. Keep in mind, the stock market includes companies like Wal-Mart, Apple, and ExxonMobil, all companies that pass inflation to their customers and receive right back for their investors.

In his note to clients on Friday, BMO Capital Markets Brian Belski also discussed this relationship between rising rates and rising stock prices. He explained that rising rates are actually sign of good things to come.

“[S]ome of the best and most consistent average returns have occurred when interest rates have risen from very low levels – as is currently the case,” Belski said. “From our perspective, this means that the bond market is correctly anticipating future economic growth and staying ahead of inflation – things that typically benefit stock prices.”

Reviewing the data since 1985, Belski found that the least favorable interest environments for stocks were when rates were low, below average, and declining.

“This makes sense to us since lower interest rates are typically reflective of sluggish economic growth and vice versa,” he said.

## Bonds

At first glance, the inverse relationship between interest rates and bond prices seems somewhat illogical, but upon closer examination, it makes sense. An easy way to grasp why bond prices move opposite to interest rates is to consider zero-coupon bonds, which don’t pay coupons but derive their value from the difference between the purchase price and the par value paid at maturity.

For instance, if a zero-coupon bond is trading at $950 and has a par value of $1,000 (paid at maturity in one year), the bond’s rate of return at the present time is approximately 5.26% ((1000-950) / 950 = 5.26%).

For a person to pay $950 for this bond, he or she must be happy with receiving a 5.26% return. But his or her satisfaction with this return depends on what else is happening in the bond market. Bond investors, like all investors, typically try to get the best return possible. If current interest rates were to rise, giving newly issued bonds a yield of 10%, then the zero-coupon bond yielding 5.26% would not only be less attractive, it wouldn’t be in demand at all. Who wants a 5.26% yield when they can get 10%? To attract demand, the price of the pre-existing zero-coupon bond would have to decrease enough to match the same return yielded by prevailing interest rates. In this instance, the bond’s price would drop from $950 (which gives a 5.26% yield) to $909 (which gives a 10% yield).

Now that we have an idea of how a bond’s price moves in relation to interest-rate changes, it’s easy to see why a bond’s price would increase if prevailing interest rates were to drop. If rates dropped to 3%, our zero-coupon bond – with its yield of 5.26% – would suddenly look very attractive. More people would buy the bond, which would push the price up until the bond’s yield matched the prevailing 3% rate. In this instance, the price of the bond would increase to approximately $970. Given this increase in price, you can see why bond-holders (the investors selling their bonds) benefit from a decrease in prevailing interest rates.

For a more detailed explanation of bond pricing and yield calculations, check out * Advanced Bond Concepts*.

Read more: Why do interest rates tend to have an inverse relationship with bond prices? | Investopedia http://www.investopedia.com/ask/answers/04/031904.asp#ixzz4FRfR4uqx

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