‘Kinked’ Capital Allocation Line

What is meant by ‘Kinked’ Capital Allocation Line (CAL)?

CAL is ‘kinked’ when investment in a complete portfolio is leverage and when the borrowing rate is greater than risk free rate.

What is CAL?

CAL is a straight line in investment opportunity set with risky assets and a risk free asset in the expected return-standard deviation graph.

What is expected return, risk premium and the standard deviation of a complete portfolio?

                                                                                                  

The expected return of a complete portfolio is denoted as

                            E(r_c) = r_f + y[E(r_p) - r_f]

Example: 
Let's say the proportion of investment budget in risky asset is y= .5 and that of risk free asset is (1-y).                        

The standard deviation of risk free asset (r_f ) = 0 and that of risky assets = 12%.

The expected return of risky asset  E(r_p) = 8%

§   The expected return of risk free asset E(r_f) = 4%

The expected return of the complete portfolio is:

                             E(r_c) =  4% + .5 (8%-4%)

                                      =  6%

The risk premium of a complete portfolio is 2%  (i.e., 2% greater return  for additional risk)

The standard deviation of a complete portfolio is 6% (= .5 x 12%) (i.e., risk has reduced by 50%).

What is the slope of CAL?

The slope of CAL (S) is the incremental return per incremental risk.  It is called reward to volatility (Sharpe) ratio.

                           

                           S = [E(r_p) –r_f ] / σ_p

                                                 

                                   = 4% /12%   = .33

Let's see what would be the slope of CAL when the portfolio has borrowed at risk free rate

Now, the proportion of investment in risky assets ‘y’ would be greater than one.

Let’s say an investor has investment budget of $2,000,000 and has borrowed $1,000,000 and plans to invest all the funds in risky asset.

                                    

                              Y = 3,000,000/2,000,000

                              Y = 1.5 and

                         (1-y) = -.5  (i.e., the proportion of risk free asset)

                                                                                  

 Other things remaining same, 

 Levered  E(r_c) = 4% + 1.5 (8%-4%) = 10%

Standard deviation of the portfolio (levered) = 1.5 x 12% = 18%

Slope of CAL (levered)    S = [E(r_c)-r_f] / σ_c

                                           = [10%-4%]/18% 

                                           = .33                                    

                                                

As long as risk free rate is equal to borrowing rate the slope of CAL will remain unaffected and CAL is straight.

Kinked CAL

Not everyone can borrow at risk free rate, particularly non-government investors. Default risk of borrowers induce lenders to charge higher rate of interest. Suppose the borrowing rate is 5% the slope of CAL now is:  

                          S = [E(r_p) – r_f] / σ_p

                             = [8% -5%]   / 12%                   

                             = .25

The reward-to-volatility ratio or the slope of CAL gets reduced from .33 to .25 and hence CAL is slightly flattened or kinked.

Financial Asset Classes

Hi,

In this blog, I am trying to explain various types of financial assets with more focus on derivatives and its variants.

Financial assets are broadly classified into equity, debt securities, and derivatives.                               

Equities or common stocks represent ownership share in the corporation.

§  Common stock holders have residual claim on the assets and income of the corporation (when the corporation is liquidated they have a last claim), and their liability is limited (creditors cannot lay claim to personal assets of the stock holder). 

§  Equity shareholders are entitled to vote and receive dividends (if declared). Returns to shareholders are tied to corporation performance.  

§  An investor can purchase share of foreign company, not directly, but through Depository Receipts. American Depository Receipts (ADRs) are certificates traded in U.S. markets representing ownership in shares of a foreign company.

Debt or fixed income securities promise to pay fixed stream of income (e.g., In a 8% 5 year bond, par value $1,000; the investor gets $80 as interest each year) or a stream of income determined by a specified formula (e.g., In a 5 year LIBOR +2% bond, par value $1,000; the investor gets interest at the prevailing LIBOR rate + 2%).

§  London Interbank Offered Rate (LIBOR) is short term interest rate at which large banks in London are willing to lend money among themselves, and it also acts as reference rate in European money market.

§  Money market securities consists of very short term, highly marketable, low risk securities (e.g., Treasury bills, Certificate of Deposits, Commercial papers, Repos and Reverses etc.)

§  Long term securities include Treasury bonds, bonds issued by federal agencies, state and local municipalities (these will be discussed separately).

A derivative security derives its value from another security’s characteristics or value. The other security is termed as underlying asset.

Derivatives have variants such as forwards, futures, options, and swaps etc.

A spot contact is an agreement to buy/sell an asset today. In contrast, a forward contract is an agreement to buy/sell an asset at an agreed (exercise) price and quantity to be delivered on or before the future agreed date (expiration date).

§  Forwards are private contracts traded in over-the-counter markets and are usually between two financial institutions or between financial institution and one of its clients. They are highly customized and usually not regulated.

Future contract, unlike forward contract, is a more formalized, legally binding agreement and are traded on registered exchanges.

§  They are highly standardized regarding quality, quantity, delivery time and location for each specified commodity.

§  Clearing house acts as counterparty to all future contracts (i.e., if one of the party to the contract fails to fulfill his/her obligation clearing house fulfills the contract either by buying/selling).

§  Futures contracts are marked to market on a daily basis (i.e., profit/loss are booked on a daily basis). The investor is required to maintain sufficient funds in margin account.

§  A long position in a futures contract is held by the trader who commits to purchase the asset on the delivery date. A trader holds short position if he/she commits to deliver the asset on delivery date.

A call option contract gives the option holder the right, but not the obligation, to buy an asset at the exercise price from the option seller within the specified time period.  

A put option contract gives the option holder the right, but not the obligation to sell an asset at the exercise price from the option buyer within the specified time period.

§  The value of an option depends upon strike (exercise) price, current stock price, time to expiration (maturity), dividends etc. To exercise or not to exercise the option depends on all these factors.

§  The buyer of option contract (both call and put) has to pay option premium. The owner of the option contract is called buyer or holder of long position, and the seller is called writer or holder of short position.

§  An American option contract can be exercised at any time between the issue date and expiration date, but a European option contract can be exercised only on the expiration date.

§  There are various trading strategies involving options (e.g., covered calls, protective puts, butterfly spreads, bull and bear spreads etc.)

A swap is an over-the-counter agreement between two entities to exchange cash flows in the future. For example, a corporation agrees to pay cash flows equal to interest at a predetermined fixed rate on a notional principal for a predetermined period. In return, it receives interest at a floating rate on the same notional principal for the same period of time. This type of swap is known as interest rate swap.

§  Currency swap involves exchange of principal and interest payments in one currency for principal and interest payments in another currency. Currency swaps are used to transform liabilities into assets.

 

 

Financial Assets Vs Real Assets

Hi,

This blog tries to explain the readers meaning of real and financial assets, how financial assets facilitate to create real assets, and the reasons why real assets alone matters in determining the net wealth of the nation.

Let me begin with the term ‘Investments’. Investments are current commitments of money and other resources in expectation of future earnings or benefits. Material wealth (also known as productive capacity) of an economy is determined by goods and services produced in that economy.

Corporations use real assets such as land, building, equipment etc. to produce goods and services. Other than these tangible assets, intangible assets such as knowledge, trademark, patents etc. are also used.

Corporations need finance to obtain real assets. Hence, to raise sufficient funds (also known as capital) they sell securities such as stocks, bonds etc. These securities have claim to the income generated by real assets or on real asset itself. These securities are known as financial assets.

Financial assets, unlike real assets, do not contribute directly to the productive capacity of the economy.

Why real assets alone matter in determining the net wealth of the nation and why not financial assets?

National wealth comprises of net wealth of all the households and corporations. Financial assets of a household usually comprises of fixed deposits with banks, stocks, bonds etc. For the issuer of such securities claims are established. Hence, financial assets and financial liabilities are aggregated (netted).

For example, when a household makes a fixed deposit with a bank an asset is created. However, for the bank it is a liability as it has created an obligation to repay the deposit at a future date. When these financial assets and liabilities are aggregated real assets alone will remains as national wealth.

In my next blog, types of financial assets will be discussed.

 

 

On-Balance Sheet Hedging and Off-Balance sheet Hedging Using Forwards

On-Balance Sheet Hedging and Off-Balance sheet Hedging Using Forwards

When is financial institution long and short in forex exposure?

FI is long when its assets are greater than liabilities and is short in exposure if its liabilities are greater than assets.

The mismatch between FI’s foreign financial asset and foreign financial liability portfolio leads to FX exposure.

How to create opportunities for higher returns in Forex market?

Banks try to exploit forex market that creates opportunities using Off-balance sheet and On-balance sheet hedging tools. This can be done either by increasing the Return on asset (ROA) or by lowering cost of funds (COF) or both.

(1)     Let’s see how Unhedged Balance Sheet is exposed to forex risk.

Let’s say a U.S based FI has USD 200m 8% CDs for one year and loaned USD 100 million in U.S at 9%, and USD100 million equivalent in U.K.loans at 15%. The exchange rate is 1GBP = $1.60.

Extract of Balance sheet

Assets	Liabilities
U.S. loans (9%)                         =  USD 100.0 m	USD  (8% CDs 1 year)                = USD 200.0 m
U.K loans (15% )                       =   GBP   62.5m (1GBP = USD1.60)

Rate of interest in U.K.is 15% and in U.S. 9%

Let’s now compute Return on Asset (ROA), Cost of Funds (COF) and Return on Investments (ROI) under two scenarios:

(1) When GBP depreciates to 1GBP = $1.45

(2) When GBP appreciates to 1GBP = $1.70

Computation of ROA, COF and ROI

	When GBP  depreciates	When GBP  appreciates
Exchange rate - end of the year	1 GBP =  1.45 USD	1 GBP = 1.70 USD
Returns from U.K Investment 62.5 x .15 = 71.875 GBP Converting back to USD we get	71.875 x  1.45 = USD 104.22 Returns in USD = 4.22%	71.875 x 1.70 = USD 122.18 Returns in USD = 22.18%
ROA	.5 x 9% + .5 x 4.22% = 6.61%	.5 x 9%+.5 x 22.18% = 15.59%
COF	= 8%	= 8%
ROA – COF = ROI	6.61% - 8% = -1.39%	15.59% - 8% = 7.59%

Inference: ROI is negative when GBP is depreciating.

 (2)     On-balance sheet hedging - When GBP is depreciating and appreciating

Continuing with our previous example, the FI has instead sold CDs equivalent to USD100 million each in U.S and U.K at 4% and 11% respectively. The extract of balance sheet is given below.

Extract of Balance sheet

Assets	Liabilities
USD 100 million U.S loans 9%	USD 100 million (U.S. 8% CDs 1 year)
USD 100 million equivalent U.K. loans 15% = 62.5 GBP	USD 100 million in U.K CD’s (11%)

Exchange rate at the beginning of  the year  1GBP = $1.60

Let’s now compute Return on Asset (ROA), Cost of Funds (COF) and Return on Investments (ROI) under two scenarios using on-balance sheet hedging:

                                        On-Balance Sheet Hedging

	When GBP  depreciates	When GBP  appreciates
Exchange rate - the end of the year Converting to GBP 100/1.60 = 62.5m Interest rate = 15%	1 GBP =  1.45 USD	1 GBP = 1.70 USD
Returns from U.K. investment GBP 62.5 x 1.15 = 71.875 Converting it to USD	71.875 x 1.45 = 104.22 Returns in USD = 4.22%	71.875 x 1.70 = 122.18 Returns in USD = 22.18%
Cost of funds (U.S Loans)	8%	8%
Cost of funds (U.K Loans) 62.5 x1.11 =69.375	69.375 x 1.45 = 110.59 Returns in USD = .59%	69.375 x 1.70 = 117.938 Returns in USD = 17.938%
Weighted average cost of funds	.5 x 8% + .5 x .59% =4.30%	.5 x 8% + .5 x 17.94% = 12.97%
Weighted return on asset portfolio	.5 x 9% + .5 x4.22% = 6.61%	.5 x 9% + .5 x 22.18 % = 15.59%
Net Return	6.61% - 4.3% = 2.31%	15.59% - 12.97% = 2.62%

Inference:

The firm can lock in positive ROI even when GBP is depreciating.

When GBP appreciates the firm can earn higher returns.

 

(3)     Balance sheet hedging using Forwards

Continuing with our previous example, suppose the bank enters into forward currency contract at 1GBP = $1.55 the ROI would be:

Exchange rate - end of the year	1 GBP = 1.55 USD
Returns from U.K Investment 62.5 x .15 = 71.875 GBP Converting back to USD we get	71.875 x 1.55 = USD 111.41 Returns in USD = 11.41%
ROA	.5 x 9%+.5 x 11.41% = 10.21%
COF	= 8%
ROA – COF = ROI	10.21% - 8%  = 2.21%

(4)   Comparison of Net Returns

Net return (ROI)	When GBP  depreciates	When GBP  appreciates
Un-hedged balance sheet	(1.39%)	7.59%
On-balance sheet hedging	2.31%	2.62%
Off-balance sheet hedging using forwards		2.21%

On-balance sheet hedging is providing higher returns when GBP appreciates compared to Off-balance sheet hedging using forwards.