13th letters to friends of Brunei (Bond Price)

Assuming you want to invest in bond for capital (& coupon) gains, with no intention to hold it to maturity. Below are some interesting facts:

1. Bond price and yield (& interest rate) are inversely related.

During economic crisis, when Fed Reserve raise the interest rate, the bond price will fall, and the yield will rise. Therefore, when some smart journalist writes about "bond yield increase .....", it (usually) is not good news.

2. Bonds with longer years to maturity is more volatile than short bonds.

Therefore, if a decrease in interest rate is expected, consider buying into long bond. On the other hand, if interest rate is expected to rise, sell long bond and buy short bond.

3. Low coupon bonds are more volatile than high coupon bonds

When decrease in interest rate is expected, consider buying into low coupon bond. If interest rate is expected to rise, sell low coupon bond and buy into high coupon bond.

4. When yield change, the size of a price increase is greater than the size of price decrease.

A 1% decrease in yield, you will enjoy gain in bond price, and this gain is more than the loss you would suffer from a 1% increase in yields.

Above facts are from Burton Malkiel's "bond price theorems".

First time reader will get confuse with the yield & bond price changes. This is normal. It took me many years of constant reading to understand the subject. Consult a qualified financial advisor if you want to invest in bonds.

12th letter to friends of Brunei (Bond's valuation: Duration)

Bond's price and yield are highly sensitive to interest rate movement. We uses the concept of "duration" to express this sensitivity. For example, what would be the expected bond price if interest move up by 2%?

Duration is a measure on how long does it take to recover your invested capital in a bond. The calculation is a bit complex, but let me illustrate with 2 examples.

If Mr. A invests $1000 into a zero coupon bond (par value $1000)with 3 years to maturity. At the end of 3rd year, Mr. A will receive $1000, and the duration is 3 years. If Mr. A invests the same amount in to an 8% coupon bond, the duration could be shorter, say 2.78 years (a rough figure). Because Mr. A has begun to receive the coupons.

The duration (D) information is used to estimate changes in bond price.

% bond price change = - D x changes in interest rates

(the -ve sign denotes the inverse relationship between bond price and interest rate movement)

Example 1: Bond A is an 8% coupon bond, par value $1000, 3 years to maturity and current price is $950.25. The duration is 2.53 years. Estimate the bond price when interest rate falls 1.5%.

% bond price change = -2.53 x -1.5% = 3.795%

Therefore, the new bond price is $950.25 x (1+ .03795) = $986.31

Example 2: Using above information, estimate the bond price if interest rate rises 0.5%.

% bond price change = -2.53 x 0.5% = -1.265%

Therefore, the new bond price is $950.25 x (1- 0.01265) = $938.23

11th letter to friends of Brunei (Bond's valuation [Part 3])

The most commonly used statistics for bond's valuation is "Yield To Maturity" (YTM). When newspaper talks about bond's yield, they are referring to YTM.

YTM will give you an estimate of the total return of the bond, assuming the bond is held to maturity and all coupons are reinvested at a rate equal to YTM.

Bond price = Coupon/(1+YTM) + coupon/(1+YTM)2 + ......coupon /(1+YTM)n+ Par value/(1+YTM)n

I myself find above formula difficult to remember, so i also rely on financial calculator to calculate YTM. The key strokes are as follows:

FV = par value of bond

PV = current bond price

PMT = annual coupon value

n = number of years to maturity (if coupon is received 2 times a year, then use n x 2)

i % = YTM

Example 1: The YTM for a zero coupon bond selling at $235 with 10 years to maturity, if it is compounded annually, is

a. 14.25%

b. 16.05%

c. 17.15%

d. 15.58%

Example 2: An 8% coupon bond has a market price of $900 and 20 years to maturity. What is its YTM?

a. 8%

b. 8.50%

c. 9.10%

d. 10%

Some interesting fact about YTM (i.e. bond's yield)

1. As bond price is fluctuating, the YTM is also a fluctuating figure.

2. When bond price is down, YTM is expected to rise.

3. When the bond price is up, the YTM will go down.

4. YTM is not an immediate return data, it simply refers to if one invest in a bond with YTM of 8%, he needs to hold the bond to maturity & reinvest the coupon at YTM in order to realise the yield.

* Example 1: Using my faithful FC-100 (Casio financial calculator). PV= -235, FV=1000, n=10, comp i%(YTM) = 15.58%. Hence, the answer is d.

** Example 2: PV = -900, FV = 1000, PMT = 80, n = 20, comp i%(YTM) = 9.10%. Hence, the answer is c.

10th letter to friends of Brunei (Bond's Valuation [part 2])

Most bonds are purchased from the secondary market. The price of such bond can be more (premium) or less (discount) than the bond par value. By dividing the coupon interest with the bond price, we would know how much interest income you will receive each year relative to the price you are paying for the bond.

Current Yield = Annual Coupon / Bond Price

Example 1: A $1,000 par value bond pays a $100 annual coupon has a price of $1,050. What is its current current yield?

a. 10.00%
b. 5.00%
c. 3.50%
d. 9.52%


Example 2: The same $1,000 par value bond that pays $100 annual coupon now has a price of $960. What is the current yield?

a. 10.00%
b. 10.42%
c. 4.00%
d. 3.50%

In these 2 examples, you will notice an interesting truth about bond yield and price. When price goes up, the yield will come down; and the reverse is true.


* The working for example 1 is $100/$1050 = 0.0952 (or 9.52%), hence the answer is d.

** The working for example 2 is $100 / $960 = 0.1042 (or 10.42%), hence the answer is b.

9th letter to friends of Brunei (Bond's valuation [part 1])

Let's talk about bonds. One of the oldest financial instrument around. The concept is simple.

A has a great business idea but is short of money. B has money. A borrows money from B, and in return promises to pay B a fixed interest for 10 years, and returns the capital to B(also at 10th year). A uses the cash flow generated from the business to pay the fixed interest to B. Here we go, we have just structured a 10 year bond product.

C learns about the contract between A and B. C proposes to B to buy over the contract at a premium or discount over the capital borrowed by A. This is the secondary market of bond.

Before we go into the mathematics, one has to know which value will change, which value will not change.

a. The par value is the maturity value of the bond. This will not change.

b. The fixed interest rate (i.e. the coupon rate) is a function of the par value will not change.

c. The market price of the bond will change, depending on the market factors like interest rate, inflation, demand and supply etc.

1. Coupon rate (or coupon yield)

Coupon rate is the annual coupon amount divided by the bond's par value.

Coupon Rate = Annual Coupon / Par Value

Example 1: What's the coupon rate of a bond with par value of $1000, paying $80 p.a.?

a. 8.0%

b. 12.5%

c. 10.0%

d. 5.0%

Example 2: Coupon rate will not change. True or false?

a. True.

b. False, coupon rate can change depending on market situation.

*For whatever reason, the bond's lingo uses "yield" instead of "return" (commonly used by equity valuation). You will see alot of "yield" in our discussion of bond valuation.

8th letter to friends of Brunei [Stock Valuation (part 5)]

Before I sign off from stock valuation, let me highlight some points.

1. Whether it is dividend discount model or P/E method, we are trying to establish an intrinsic value of a stock.

2. This intrinsic value (of the stock) is then compared with the current price of the stock.

3. If the intrinsic value is more than the current price of the stock, then the stock is undervalued, which could lead to a "buy" decision.

4. If the intrinsic value is less than the current price of the stock, then the stock is overvalued, which could lead to a "sell" decision.

5. Financial analysts commonly refer high P/E stocks as "growth stocks", low P/E stocks as "value stocks".

6. P/E ratios are the most comonly used, but it is not a perfect ratio. For example, if the the earnings are low or negative.

7. The other less common, but equally sound, ratios are:

a. Price-Sales Ratio (PSR) = Market Value of Company / Last year's sales

(market value of company = stock price x total stock outstanding)

b. Price-Cash Flow Ratio (PCF) = Market Value of Company / Operating cash flow

c. Price-Book Ratio = Market Value of Company / Stockholders' equity

(Stockholders' equity = Total Assets - Total Liabilities)

Cheers!

7th letter to friends of Brunei [Stock Valuation (part 4)]

The most common way to value a stock is through Price-Earning (P/E) ratio. Using the current P/E ratio x Estimated earning for the next 1 year will give an estimated intrinsic value of a stock. Let me first explain P/E ratio.

There are 2 ways of calculating P/E of a stock.

1. The accounting method

This method uses the current price of the stock divide by the immediate past year earning per stock. For example, if the company has the following performance:

Sales $2.0M

Expense -$1.5M

Earnings $0.5M

Assuming company has 1M stocks outstanding.

The Earning Per Stock (EPS) is $0.5M/1M = $0.50 per stock

If the Price Per Stock is $10, then the P/E = $10 / $0.5 = 20

This method is simple, but one has to take note that this method uses historical data (i.e. past earnings) which sometime might not give an accurate indication in the future. Especially if the company's business is highly volatile.

2. The Dividend Discounted Method (DDM)

The other method is to derive P/E from the DDM formula which we learn earlier.

Po = D1 / [k -g]

Let's divide E1 by both side,

Po/E1 = (D1/E1) /[k-g], where (D1 / E1) is actually the Dividend Payout Ratio (DPR)

Therefore, P/E = DPR / (k-g)

(This method is forward looking as compared to the accounting method.)

The intrinsic value of stock (Po) = E1 x DPR /(k-g)

Example: The Lego Corporation currently has earnings that are $4 per stock. In recent years earning have been growing at a rate of 7.5%. If the Lego Corporation has a retention rate of 40% & a required rate of return of 14%, what is the current intrinsic value of the stock?

Estimated earning for the next 1 year (E1) = $4 (1+0.075) = $4.3

DPR = (1 - Retention Rate) = (1 - 0.4) = 0.6

k - g = 0.14 - 0.075 = 0.065

Therefore, intrinsic value of stock (Po) = E1 x DPR /(k-g) = $4.3 x (0.6 / 0.065) = $39.69

Exercise: The Miller Corporation has current earning per stock of $6. Assume a dividend payout ratio of 55%. Earnings grow at a rate of 8.5%. If Miller's required rate of return is 15%, what is its current(intrinsic) value?

a. $51.33

b. $55.08

c. $57.02

d. $52.05

You can do this exercise, you would have understood the concept.

6th letter to friends of Brunei [Stock Valuation (part 3]

In calculating intrinsic value of a stock, we need to know the dividend "growth rate" (g), or sometimes known as sustainable growth rate. This growth rate can be calculated as follows:

g = Return on Equity (ROE) x Retention Ratio.

Let me explain the easier term, which is ROE. It is the net income of a company divided by common stockholders' equity, mathematically it is:

ROE = Net Income / Equity.

Retention ratio is the proportion of earning retained after dividends are being paid out. This sounds complicated, let me illustrate in a comical way. Let's assume dividend as the amount a man need to give his wife from his income (i.e. earnings). For every $1000 this man earns, he gives $800 to his wife, then the Dividend Payout Ratio (DPR) is $800/$1,000 = 0.8. How much has this man "retained" the earning for himself? The answer is $200, the retention ratio is 1-0.8 = 0.2.

Retention ratio is therefore expressed as 1 - DPR (or dividend payout ratio)

Example: ABC Co's return on equity is 12%. Earnings per stock was $4, and a per stock dividend of $1 was paid out. What is ABC Co's retention ratio and its sustainable growth rate?

Dividend Payout Ratio(DPR) = $1 / $4 = 0.25

Retention Ratio(RR) = 1 - DPR = 1- 0.25 = 0.75

Sustainable Growth Rate (g) = ROE x RR = 0.12 x 0.75 = 0.09 (or 9%)

5th letter to friends of Brunei [Stock Valuation (part 2)]

As you can see from the previous blog entry, the dividend discounted model method of calculating intrinsic value of a stock has two important variables:

1. k = Required Rate of Return of the stock;
2. g = The (Sustainable) Growth Rate.

Let me explain further:

1. Required Rate of Return (k)

Assuming there is risk free investment product which gives you 2.5% return. If you wish to invest into another stock, obviously you will expect this stock to give you a return above the risk free rate. This expected addition return rate is known as risk premium. Mathematically, this is:

k = Risk free rate + risk premium rate

Risk premium = beta x (historical return of stock in the market - risk free rate)

= beta (Rm - Rf )

Beta is the sensitivity of the stock compared to a stock market index(e.g. STI or S & P 500).

For example: S'pore T-bill has a yield of 2.5%. Assuming RHB bank has a stock beta of 1.4 and has a historical return of 6%, RHB bank's required rate of return is:

k (RHB bank) = R (t-bill) + beta (Rm - Rf) = 2.5% + 1.4 (6%-2.5%) = 7.4%

Incidentally, the formulae for calculating k is also known as the Capital Asset Pricing Model (CAPM), which is an important formulae used in portfolio management.

4th letter to friends of Brunei [Stock Valutation (part 1)]

Assuming you are a fund manager of Singapore Growth Fund. How would you ascertain the intrinsic value of stocks in your portfolio? There are two ways of doing this. One by calculating the present value of the cash dividends of the stock; two by examining the earnings of the stock.

1. Present value of cash dividends [also known as Dividend Discount Model (DDM)]

Let's assume the stock will pay the same dividend year after year, for example a preference share. This is called zero-growth model. The intrinsic value of this stock can be calculated as follows:

P0 = d / k
P0 = Intrinsic value of stock
d = Fixed dividend expected for all future periods
k = Required rate of return for this stock.

Consider a preference share with a par value of $10 that pays a fixed dividend of 50 cents per share. If the required rate of return for this stock is 8%, then its intrinsic value is:

P0 = d / k = $0.50 / 0.08 = $6.25

What if the stock has a constant growth in dividend? Then we have slightly more steps to do. First, we need to calculate the dividend in the next period. Second, we divide this dividend value with [required rate of return – dividend growth rate].

P0 = d1 / (k – g)
d1 = Dividend in the next period [i.e. D0(1+g)]
k = Required rate of return
g = Dividend growth rate

Let's do one example: The Krehbiel Corporation 's required rate of return is 10%. Krehbiel's current cash dividends per share are $2.50 and have been growing at 3% per year. What do you expect the stock price will be?

Krehbiel Corp's Stock price (P0) = $2.5(1+ 0.03) / [0.1 – 0.03] = $2.575 / 0.07 = $36.79

What if the dividend rate has declined in the next year? No problem, let's look at another example: The Tucker Mining Company has been experiencing a 6% per year decline in its cash dividend growth rate for the past few years; this decline is expected to continue. Tucker has a current dividend per share of $3. If Tucker's required rate of return is 14.5%, what is a share of the stock worth?

Tucker Co's Stock price (P0) = $3(1+ -0.06) / [0.145 – (-0.06)] = $2.82 / 0.205 = $13.76

3rd letter to friends of Brunei (Standard Deviation)

In investment planning, the actual return can exceed or less than expected return (or average return). Such variability is known as risk. One of the most important measurements of risk is “standard deviation” (or σ).

The formula for σ is √ [sum of (actual return – average return) 2 / (number of data – 1)]

Let me illustrate using the following data:

Year 1, 2, 3, 4, 5

Return 40%, 25%, -20%, -30%, 30%

The average return of above data is = [0.4+ 0.25 + - 0.2 + - 0.3 + 0.3] / 5 = 0.09 (or 9%)

The sum of (actual return – average return) 2 is

(0.4 – 0.09)2 + (0.25 – 0.09)2 + (-0.2 – 0.09)2 + (-0.3 – 0.09)2 + (0.3 – 0.09)2 = 0.402

Number of data – 1 = 5 -1 = 4

Therefore, σ = √ [0.402 / 4] = 0.31 (or 31%)

2nd letter to friends of Brunei (Measuring Returns over multiple period)

Measuring returns (of investments) over multiple periods builds on the earlier blog entry on total return and relative return. There are 3 common ways of measuing such returns. They are:

1. Cumulative Wealth Index (CWI)

2. Arithmetic Mean (AM)

3. Geometric Mean (GM)

Let's assume you invested into a stock for 5 years as follows:

Year 1, 2, 3, 4, 5

Total Return (TR) 40%, 25%, -20%, -30%, 30%

Relative Return (RR) 1.4, 1.25, 0.8, 0.7, 1.3

Item 1. Cumulative Wealth Index (CWI)

CWI tells you how much you will receive today for every dollar you invested 5 years ago. The formula for CWI is to mulitply all the relative return data. [i.e. (RR1)(RR2)(RR3)(RR4)(RR5)]

In above question, the CWI is (1.4)(1.25)(0.8)(0.7)(1.3) = 1.274.

It means when you invest $1,000 in year 1, you get $1,274 in year 5.

Item 2. Arithmetic Mean (AM)

AM is a measure to help you gauge the return on an average basis. The formula for AM is [sum of total returns / number of total returns].

In above question, the AM is [{40+25+(-20)+(-30)+30} / 5] = 9%

It means if you randomly compare any one-year period within the 5 years of investment, the average return is 9%. (Be careful, sometime AM does not make sense on first look. It merely give you an average return over any 1-year period of a series of years of investment)

Item 3. Geometric Mean (GM)

GM is a measure to help you gauage the return on an annual basis. This is the most common return that appears on professionally managed fund's (e.g. Unit Trusts) factsheet. The formula for GM is {[product of the Relative Returns] }nth root - 1 , where n is the total number of data.

In above question, the GM is

{[1.4 x 1.25 x 0.8 x 0.7 x 1.3]} 1/5 - 1 = 1.0496 - 1 = 0.0496 (or 4.96%)

It means the annual return for this investment is 4.96% p.a.

It is interesting to note that mathematically, AM is either equal or always greater (in value) than GM.

1st letter to friends of Brunei(Total Return and Relative Return)

Dear friends from Brunei,

Thank you for hosting me at your bank's training centre last Friday and Saturday. I am grateful at the opportunity to lecture you on investment planning subject. As promised, I am writing these blogs to help you reinforce the calculation concepts which many of you were concerned about.

Topic 4: The Risks & Returns from investing

There are 2 ways of measuring returns & risks. One is measuring such items OVER A SINGLE PERIOD, the other is measuring them OVER MULTIPLE PERIODS.

a. Returns over a single period

Total Return (TR) = Income + Capital Gain (or Loss)

TR = (Income + Capital Gain (or loss)) / Purchase Price of stock

Relative Return (RR) = 1+ TR

For example:

i. What is the total return for a stock purchased at $36, held for one year during which $4 in Dividends was received, and sold for $30?

a. -5.6%
b. -11.1%
c. -16.7%
d. -27.8%

ii. Suppose you bought shares of ABC Co on 1 Jan for $50 each. Over the year, ABC paid cash dividends of $6.50 per share. On 31 Dec, you sold your shares at $63.50. Calculate the following:

a. Total Return
b. Relative Return

Let's try these 2 exercises, once you got it, you have mastered the concepts of total returns and relative returns over a single period (i.e. for 1 year). The next blog, I will explain measuring returns over multiple periods (i.e. from year 1 to year 5 for example)

Are we trying to do too much?

I am now recovering from flu, and have the luxury in many years to rest. I mean truly resting, without having to think of activities to do on Sunday with people. Too much activities and un-checked responsibilities can drive a person to behave otherwise.

Today’s papers wrote about the profile of a potential maid abuser. I am not surprise to find stress and inability to cope with life’s activities is the common denominator of a maid abuser. I believe no body wants to be a maid abuser, but as one is being overwhelmed and stressed out by life’s problems, the devil in us can control us. If this is left un-checked, unfortunate (and sometime fatal) event can happen.

What can we do? While I don’t profess to be an expert in human affairs, I do subscribe to a few rules which I like to share:

1. Learn to accept that I am not the master of world. In fact, I exist to make the world a little better for the person next door.

2. Learn to live with life’s imperfection. Perfection is the job of the creator, whom I am not.

3. Learn to constantly consume less than I am currently consuming, like food, TV, Internet, transportation.

4. Learn to constantly engage more with people meaningfully, lend a listening ear, and a pat on the shoulder.

5. Learn to let people know my limitation. A “real me” is always better than to pretend to be a “great me”.

6. Learn to cry during life’s loss (I always do this in the washroom privately), and laugh during life’s gain.

7. Learn to let go and don’t look back.

Cheers!