Posts Tagged ‘interest rates’

How much higher can bonds go?

August 2, 2011 Leave a comment

In case you haven’t noticed, the TSX is down 5% YTD and 10% from April 2011 highs… which puts it squarely in a typical correction territory… while Bonds (as represented by XBB – DEX Universe Bond Index) are up 2.5% and 4.25% for the same period as illustrated by the TSX/XBB weekly charts

Here is look at the bond performance over the past decade… and today XBB gaped up!

The question is not how low can stocks go but rather how much higher can bonds go?

Bond prices are inversely related to interest rates i.e. if bonds are rising then interest rates/yields are falling… for all intents and purposes, XBB reflects all rates along the yield curve i.e. short and long term rates…

short term rates are above their record lows but 1% is still low historically

10 yr GOC yield is at 2.8%… which is ~10 bp higher than the most recent low of 2.68% from a year ago

So there is room for bonds to go up further especially considering the Euro area weakness… but will we see new lows in 10-year yields?

(in case you are wondering why the 10-year yields… the trend of 10-year yields is usually considered a good barometer of future economic growth)


CFA Reading on Derivatives – FRA and Futures Markets & Contracts

May 10, 2011 1 comment

CFA Level 2 – Derivatives; Study Session 16, Reading 61 in 2011 curriculum/Reading 59 in 2010 – Futures Markets & Contracts

I will go over FRAs and Futures in this post. (FRA is part of previous reading)

Forward Rate Agreements (FRA)

FRA is yet another derivative product. The underlying in an FRA is an interest rate on a deposit or on a loan i.e. the price of an FRA is an interest rate. The deposit/loan can be for any period in the future and the beginning of this period can also be any period in the future. It is the beginning and ending of these periods that form the notation of an FRA.

For example, 2 x 5 FRA means that the derivative contract expires in 2 months and the underlying deposit or loan is initiated at the end of 2 months (from now) and ends at the end of 5 months (from now) i.e. the deposit/loan period is for 5 – 2 = 3 months and (it is worth repeating) those 3 months start 2 months from now. (confusing I know but it is imperative you get your head around this)

An FRA is a forward contract in which the long, agrees to pay a fixed interest payment at a future date and receive an interest payment at a rate to be determined at expiration of the contract (not the expiration of the deposit/loan).

Value of an FRA from CFA Institute:

The value of an FRA based on a Eurodollar deposit is the present value of $1 to be received at expiration minus the present value of $1 plus the FRA rate to be received at the maturity date of the Eurodollar deposit on which the FRA is based, with appropriate (days/360) adjustments.

The payment made at the expiration of the FRA is the difference between the Value of the FRA and the agreed upon price of the FRA, adjusted by the notional principal and the number of days.

The payoff is also discounted, however, to reflect the fact that the underlying rate on which the instrument is based assumes that payment will occur at a later date… remember that the period of deposit/loan starts at the expiration of the FRA contract and the interest payment on this deposit/loan is made at the end of the period.

Let’s move on to Futures Markets and begin by establishing the difference between Futures & Forwards

Figure 2

Pricing Futures is similar to Forwards, future price for an asset with no storage costs is given by:

The market price of a Forward contract is the amount a party to the transaction is willing to pay to terminate the contract. However, because futures are traded on an exchange and are settled and marked-to-market daily , the Futures contract have zero value at the end of the day and have non-zero value during the day.

Value of a futures contract = Current Futures price – Futures price at last mark-to-market

Because of the daily settlement feature of futures, cash is exchanged daily between the long and the short and this cash can be invested to earn a return. And because of this futures prices are sometimes higher than forwards for an identical contract.

The following table illustrates the difference:

Costs & Benefits of holding the underlying asset

If holding an underlying asset results in monetary costs and benefits (net cost), futures price is:.

If holding an underlying asset results in non-monetary benefits (convenience yield), futures price is:

All other formulas (dividend paying asset, coupon paying asset, etc) for pricing futures are similar to forwards.

In the next topic, I will discuss contango and backwardation.

Source of all formulas: Schweser Notes

What is the theoretical relation among various rates in Economics?

May 7, 2011 2 comments

I have been reviewing study session 4 in CFA Level 2 Economics and I can’t seem to get my head around all the parity relations… hence a post to clarify my thoughts and develop a clear understanding.

All parity relations are a function of exchange rates, nominal interest rates, real interest rates and inflation rates between the a pair of countries/currencies.

Interest Rate Parity – Exchange Rate > Nominal Interest Rate

Covered Interest Rate Parity:

forward exchange rate as a function of the spot exchange rate and nominal interest rates.

Uncovered Interest Rate Parity:

expected spot exchange rate as a function of the current spot exchange rate and nominal interest rates

International Fischer Relation – Inflation Rate > Nominal Interest Rate

difference in nominal interest rates should be equal to difference in expected inflation rates because real rates as equal

Purchasing Power Parity (PPP) – Exchange Rate > Inflation Rate

Absolute PPP

price of a basket of similar goods between two countries should be equal (rarely is in practice)

Relative PPP

expected spot exchange rate as a function of the current spot exchange rate and inflation rates (note similarity to uncovered interest rate parity)

Approximate Relative PPP

difference in inflation rates is equal to the expected appreciation/depreciation of the currency

The above stuff is easy on its own but gets tricky when combined with International Asset Pricing reading from study session 18 on Portfolio Management.

Real Exchange Rate

explains the changes in nominal exchange rate not explained by the difference in price levels i.e.

(Note here that the price levels are already adjusted for inflation, hence if real exchange rates are constant then any change in nominal exchange rate is explained by the difference in inflation)


% Change in Real Exchange Rate = % Change in Nominal Exchange rate – (Inflation in DC – Inflation in FC)

Foreign Currency Risk Premium – Exchange Rate > Real Interest rates

is the difference between the % change in exchange rates and the difference in real interest rates

I think that should clarify the interplay of different rates.

CFA Reading on Derivatives – Forward Markets & Contracts

April 12, 2011 1 comment

CFA Level 2 – Derivatives; Study Session 16, Reading 60 in 2011 curriculum/Reading 58 in 2010 – Forward Markets & Contracts

According to the Schweser, most people find the Derivatives topic to be the most difficult in Level 2 … I find it fun and relatively easy (perhaps because I want to work in the dazzling world of derivatives)… Because you need to understand forwards to understands futures and swaps, this will be a long post.

The key to derivatives is to understand how the price of the underlying asset and interest rates influence the value of the derivative…read on and it will be clear.

What is a Forward contract?

The following is verbatim from the CFA curriculum and I think it is succinct and to the point.

The holder of a long forward contract (the “long”) is obligated to take delivery of the underlying asset and pay the forward price at expiration. The holder of a short forward contract (the “short”) is obligated to deliver the underlying asset and accept payment of the forward price at expiration.

At expiration, a forward contract can be terminated by having the short make delivery of asset to the long or having the long and short exchange the equivalent cash value. If the asset is worth more (less) than the forward price, the short (long) pays the long (short) the cash difference between the market price or rate and the price or rate agreed on in the contract.

A party can terminate a forward contract prior to expiration by entering into an opposite transaction with the same or a different counterparty. It is possible to leave both the original and new transactions in place, thereby leaving both transactions subject to credit risk [counterparty risk], or to have the two transactions cancel each other. In the latter case, the party owing the greater amount pays the market value to the other party, resulting in the elimination of the remaining credit risk. This elimination can be achieved, however, only if the counterparty to the second transaction is the same counterparty as in the first.

What is the price and value of a forward contract?

The forward price is the price that a long will pay the short at expiration and expect the short to deliver the asset. There is no cash exchange at the beginning of the contract and hence the value of the contract at initiation is zero.

The value of a forward contract after initiation and during the term of the contract as the price of the underlying asset (S) changes. The value (profit/loss) of a forward contract between initiation and expiration is the current price of the asset less the present value of the forward price (at expiration).

Here is a payoff chart of a long position in a forward contract

The value or payoff of a short position is the opposite of the long i.e. if long is valued at +10, short is valued at -10… this is true for all derivatives because derivatives are a zero-sum game i.e. one’s gain is another’s loss.

Why we need to value forward contracts:

Valuation of a forward contract is important because 1) it makes good business sense to know the values of future commitments, 2) accounting rules require that forward contracts be accounted for in income statements and balance sheets, 3) the value gives a good measure of the credit exposure, and 4) the value can be used to determine the amount of money one party would have to pay another party to terminate a position.

Formulas to calculate Forward Price and to value forward contract

  • General formula (for security without cash flows i.e. dividends, interest, etc):

Calculating the forward price of a security with cash flow includes one additional which is either the present or future value of the cash flow discounted at the risk free rate.

  • FP of an equity security (can be stocks, stock portfolios or stock indices) with discrete dividends:

Vt (value of a long position at time t)


  • FP of a fixed income security (Instead of dividends, we adjust coupons, in reality there are adjustments for special features i.e. call, put, convertible, etc):

Vt (value of a long position at time t)

(note that forward contracts on bonds must expire before the bond’s maturity, no point buying a bond on maturity)


  • FP of an equity index or a continuous compounding security (instead of a discrete cash flow, we assume continuous cash flow)

Vt (value of a long position at time t)


  • FP of a currency forward contract = forward exchange rate quoted as domestic currency/foreign currency (remember that currency units are always quoted in terms of another currency i.e. CADUSD = USD/CAD where USD = Domestic Currency & CAD = Foreign Currency)

(Hint: numerator interest rate corresponds to currency of numerator, for example if spot price was quoted as USD/CAD, the RDC = USD interest rate & RFC = CAD interest rate). In words of CFA Institute:

The [forward]price, which is actually an exchange rate, of a forward contract on a currency is the spot rate discounted at the foreign interest rate over the life of the contract and then compounded at the domestic interest rate to the expiration date of the contract.

Vt (value of a long position at time t)

… next post will cover FRAs and Futures Markets & Contract

Interest rates on bonds & mortgages

March 12, 2011 2 comments

Government of Canada (GOC) Bond Yields…slowly & surely creeping up…Notice the ‘U-shaped’ turnaround for terms longer than 1 year… noticeable in the 5yr term.

If you prefer the yield curve… which is a subset of the above data but presented differently

Fixed Mortgage Rates are based off of the respective GOC bond yields…(figure 1). The solid lines (right axis) in the figure below is the difference between the GOC bond yield and the corresponding term mortgage rate. This chart illustrates that mortgage rates don’t change as frequently as bond yields do. Look at the difference between the 3yr bond yield and the 3yr mortgage rate, it is sloping down or in other words hasn’t risen as much as the 3yr bond yields.

Is Canadian Housing the Next Domino?

March 7, 2011 1 comment

Canada’s Housing Market received plenty of international attention last week from the revered The Economist and Australia’s Business Spectator… with that kind of attention, is it time to short Canadian real-estate?

Similarities between Canada & Australia:

  • net commodity exporters
  • have similar net immigration rates
  • largely avoided the 2008-2010 financial crisis
  • have highly rated banking systems
  • housing market in a potential bubble or is it sound fundamentals

From Business Spectator [emphasis mine]:

Canadian home values have risen strongly relative to incomes and rents over the past ten years on the back of sharply rising debt levels. The key charts pertaining to the Canadian housing market are below, taken from Capital Economics’ recent Canadian housing and economic updates.

The house price growth of Canada’s major cities compared to Australia’s capital cities is shown below (chart courtesy of World Housing Bubble, here and here).

As you can see, there are some striking similarities between the two countries’ housing markets. First, the two mineral rich cities of Perth and Calgary experienced their own unique house price booms during the 2006/07 commodities bubble. Second, both countries’ governments and central banks were highly successful in reflating their respective housing markets after brief falls during the onset of the global recession.

In Australia’s case, the housing market was reflated by a combination of significantly reduced interest rates, the temporary increase in the first home owners’ grant, cash handouts to households, and the temporary relaxation of foreign ownership rules.

Canada’s central bank and government also provided significant stimulus to the housing market. In addition to the Bank of Canada lowering interest rates to record lows (click to view chart), the government significantly loosened mortgage eligibility criteria, culminating in the introduction of the zero-deposit, 40-year mortgage in 2007. Further, the amount that Canadians could borrow was increased, with many individuals in 2009 being granted loans in the $C500,000 to $C800,000 range, provided their household income ranged from $C110,000 to $C170,000.

One of the many reasons cited for the US housing bubble was low interest rates for a long period, during Alan Greenspan’s era, circa 2005… In Canada, interest rates were at their lowest ever (BOC overnight target rate of 0.25%) from April 2009 to June 2010…During this period, house prices rose about 20%… and presumably a greater than normal share of new mortgages were variable rate mortgages…

Not only was the monetary incentive high but the government loosened the qualifying standards…

Finally, in an effort to support the housing market in 2008 (when affordability fell sharply and the economy stalled), the Canadian government directed the Canadian Mortgage and Housing Corporation – the government-owned guarantor of high loan-to-value-ratio mortgages (explained here) – to approve as many high-risk borrowers as possible in order to keep credit flowing. As a result, the approval rate for these risky loans went from 33 per cent in 2007 to 42 per cent in 2008. By mid-2007, the average Canadian home buyer who took out a mortgage had only 6 per cent equity in their home, suggesting the risk of negative equity is high even if there is only a moderate correction.

This is the key….if the government did not step-in to stimulate the housing market during the throes of the recession, either Canada would have had the necessary downward adjustment to house prices, due to the negative feedback loop and possibly throw the economy in to deflation or was the government’s decision to stimulate and incentivize Canadians to buy real-estate now and worry about potential accelerated house price inflation later? Was the government in a Catch 22?

The Canadian government has since raised the mortgage eligibility criteria. In October 2008, it discontinued the zero down, 40-year mortgage, reverting back to the 5 per cent down, 35-year mortgage requirement that was in place prior to the global recession. Then, last month, the Canadian government announced that it would reduce the maximum amortisation period for mortgages to 30 years from March, adding around $100 in extra loan repayments to the average mortgage. The government also reduced the maximum amount that Canadians could borrow against the value of their homes – called a Home Equity Line of Credit (HELOC) – from 90 per cent to 85 per cent.

Perhaps, the government was in a Catch 22… and that is why it intervened to tighten mortgage rules twice in less than 1 year… The big question is: Are these changes enough or is it too little too late to control the animal spirits? And will Canadian real-estate slow down after March 18?

…Capital Economics released its Canada Economic Outlook Report (Q1 2010), which predicts sharp falls in Canadian house prices, household deleveraging, and anaemic economic growth into the future.

The report warns that Canadians’ belief that their economy is somehow invincible after emerging from the crisis relatively unscathed is “disconcerting” as house prices lose touch with fundamentals.

This is certainly true at the ground level… how much can be attributed to wealth effect from house prices increases?

“Relative to incomes, our calculations suggest that Canadian housing is now just under 40 per cent over-valued, which is about the same level of excess that the US market reached before it collapsed. We have pencilled in a 25 per cent cumulative decline in house prices over three years, mirroring what happened south of the border.

“The biggest downside risk is that an adverse feedback loop could develop, as it did in the US, with rapidly falling house prices leading to a contraction in both output and employment, which puts even more downward pressure on house prices.”

Capital Economics also warns that the government-owned CMHC could be exposed to significant losses should house prices fall significantly.

“According to our reading of CMHC financial statements, insured mortgages and securitised mortgage guarantees total an amount close to $C800 billion. The total equity of CMHC is $C10 billion.

“If house prices collapse further than we predict, say by 35 per cent, with a default rate of 10 per cent and average home equity of 10 per cent, then the potential capital loss amounts to $C20 billion.

“Even if we assume that half of this amount is eventually recovered, that still leaves an expected loss of around $C10 billion. Under the same assumptions, the 25 per cent decline in house prices that we expect over the next few years would still result in a considerable loss of around $C6 billion.”

Only a year ago, the mainstream view in Canada was that the housing market was bullet-proof and that a US-style meltdown was highly improbable. Now sentiment appears to have changed following a collapse of sales, a build-up of inventory, and three consecutive months of price falls between September and November (December recorded a 0.3 per cent rise).

Have we Canadians taken comfort in the wide-spread belief that because Canada avoided the global recession that started in the US housing sector , Canadian housing cannot slowdown or experience a US/UK/Ireland like crash?

Affordability, GDS, TDS, personal income – gross vs disposable

March 1, 2011 Leave a comment

All financial institutions and creditors use Gross Debt Service & Total Debt Service (GDS & TDS) ratios when evaluating a potential borrower for a mortgage… and at least use the TDS for all other personal loans i.e. personal line of credit, credit card, an auto-loan, a mortgage, and the kitchen sink, etc (except student loans)

Here is a short definition of GDS & TDS:

Gross Debt Service (GDS): The percentage of the borrower’s gross monthly income that is needed to pay all required monthly housing costs (mortgage payments, property taxes, heat and 50% of condo fees).

Total Debt Service (TDS): The percentage of the borrower’s gross monthly income that is needed to cover housing costs (GDS) plus any other monthly obligations that an individual has, such as credit card payments and car payments.

According to personal finance rules of thumb, courtesy of CMHC:

  • Max GDS = 32%
  • Max TDS = 40%

What is my point?

Why do creditors use gross personal income and not your after tax income or your take home pay? After all, the cost of borrowed money i.e. interest is not tax deductible in Canada (with a few exceptions)… which means that you service your debt payments from your after tax salary i.e. your take home pay and not your gross salary!

Perhaps there is a simple answer…?

Why does it matter? Because…

Using gross income in any affordability measure overstates the affordability by the tax rate… and gives the false perception that that debt is affordable when it reality it is not. The government is not going to reduce your tax so you can pay your debt (unless you are a bank)!

After every new housing affordability report in the last year, CREA has been quick to announce that housing in Canada is more affordable than ever? Really? If you believe you the horn tooting dimwits at CREA, I don’t know who can help you!…I have talked about housing affordability measure before

On to greener pastures

A recent household debt report from TD squarely puts things into perspective… I have put together a chart of Debt-to-Income & House Price-to-Income ratio vs Bank of Canada rate using the TD data…

Source: Bank of Canada, TD Bank


Note that TD uses personal disposable income in both the ratios above…

See the trend… inverse correlation between Debt-to-income/House Price-to-Income and Interest Rates? Here is the correlation matrix:

BOC Rate (left) Debt-to-Income (right) Home Price-to-Income Ratio (left)
BOC Rate (left) 1
Debt-to-Income (right) -0.57808 1
Home Price-to-Income Ratio (left) -0.49056 0.809653 1

As debt becomes cheaper (lower interest rates), demand for debt increases (green line)… isn’t that econ 101? Not sure how ugly it will be when it debt becomes expensive… relatively

As it becomes easier to get debt, debt financed assets i.e. homes increase in demand & price (purple line)